The Mariners dominated for most of the game and claimed all three points through goals from Shaun Pearson, Ross Hannah and substitute Nathan Arnold.
Pearson’s header had the hosts ahead at half-time and Hannah doubled their advantage soon after the restart.
Hannah had the chance to make it 3-0 from the penalty spot but his kick was saved by Worsnop, although Arnold did eventually grab Town’s third goal in added time.
One change was made to the Grimsby side that won at Kidderminster last time out, as goalscorer Rhys Oates was rewarded with a start.
The Barnsley loanee replaced captain Craig Disley in the XI as boss Paul Hurst switched to a 4-4-2 formation.
James McKeown started in goal, with Danny Parslow, Pearson, Toto Nsiala and Carl Magnay forming the defence.
Jack Mackreth, Craig Clay, Scott Brown and Scott Neilson were the midfielders, with Hannah joining Oates in attack.
On the bench, there were returns from injury for Lenell John-Lewis and Arnold, alongside Disley, Paul Walker and Patrick McLaughlin.
Chester made the trip east buoyed by their last-gasp derby victory over fierce rivals Wrexham on Monday.
Steve Burr’s side would look to midfielder John Rooney and pacy attacker Ibou Touray to cause problems for the home defence.
Chester won an early free kick when Craig Mahon was brought down by Clay but Rooney’s ball was cleared.
Oates had the first shot of the game for the Mariners after a neat turn to work some space but he lifted the ball over the bar.
At the other end, a shot by midfielder Kingsley James was blocked by Nsiala, before Hannah did well to beat his man and cut back into the box but missed the target at the far post.
Rooney tried his luck with a speculative effort from 35 yards after spotting McKeown off his line on nine minutes but the ball went over the bar.
Hannah then found himself one-on-one with Worsnop after beating defender Michael Kay, although he could only hit Worsnop with his shot.
A push by Rooney on Clay gave Town a free kick inside the Chester half and Neilson’s delivery was headed on by Nsiala but Worsnop was able to stop it.
A one-two between Hannah and Mackreth sent the former Macclesfield winger away through the middle but Kay got back to make a good challenge and halt the attack.
A Chester corner came soon afterwards but ultimately, it did not cause any problems for McKeown, as Rooney sent a cross out at the far post after his initial delivery was cleared back to him.
A Clay strike from 30 yards took a deflection and went out for a Grimsby corner on the right on 18 minutes and from it, the Mariners took the lead when Brown’s delivery was met by PEARSON, who headed home.
Chester then had a spell of pressure which culminated in a good chance when Rooney’s cross found striker Craig Hobson, although his free header lacked the power and direction to beat McKeown.
A foul on Hobson by Nsiala gave Chester a free kick on the left on 26 minutes but Rooney’s delivery was adjudged to have gone out of play at the far post before defender Ben Heneghan headed it back across goal.
Sean McConville volleyed a shot for the visitors after collecting the ball from a throw-in but the effort was comfortable for McKeown, who had been largely untroubled over the course of the opening half-hour.
Neilson’s chip to the near post was headed behind for a corner, which saw Mackreth shoot wide after Brown picked him out on the edge of the penalty area. Hannah was pushed to the ground by James on the left to give Town a free kick level with the 18-yard line.
A corner then came at the other end on 33 minutes and Rooney’s delivery looked set to cause problems in the six-yard box but no attacker could prod it towards goal.
He was replaced by Wayne Riley. Chester made the first substitution nine minutes before the break when left-back Gareth Roberts was forced off after picking up an injury.
McConville hit a shot over the bar for the away side, before a low drive from Magnay at the other end went past the far post.
Hobson was fouled to give Chester a free kick on the right but Ibou Touray’s delivery was cleared.
Mackreth then won a corner off Heneghan on the Town left but Brown’s kick was headed away by James.
Hannah’s free kick was met by Pearson but he could not direct his header towards goal and the ball was eventually cleared to Magnay, who fired wide from long range. Kay was the first player to be shown the yellow card with three minutes to go before half-time, when he brought Clay down near the right touchline.
One added minute was played at the end of the half and with no further chances for either side, Town retained their one-goal advantage at the interval.
Chester had shown early signs of promise but the hosts had done most of the attacking throughout the 45 minutes and deserved their lead.
No changes were made before the restart and Town looked to have the first opening when a through-ball from Brown found Hannah but the striker was flagged offside.
The Mariners doubled their lead four minutes in, when brilliant persistence from HANNAH saw him force his way into the box before working an opening and firing a left-footed shot past Worsnop and into the far corner of the net.
Hannah had another chance soon afterwards but this time, his shot was blocked by the keeper.
A golden chance to make it 3-0 came on 55 minutes, after Magnay saw a shot deflected away for a corner after a lay-off from Neilson.
Hannah could not take advantage though, as Worsnop got down to make the stop after the striker shot down the middle. Brown’s delivery was cleared back to him and after the midfielder crossed again, Mackreth was brought down inside the box and the referee pointed to the penalty spot.
The second Chester change saw Jaden Hall replace Hobson up front for the visitors, before Danny Harrison came on for Kay in Steve Burr’s final substitution.
McKeown was forced into action from a 25-yard free kick taken by Rooney but the Town keeper dived and held the ball.
The away side were almost gifted a way back into the game when a short back-pass from Nsiala was hit against McConville by McKeown but luckily for the hosts, it ricocheted wide.
A handball decision gave Town a free kick on the right edge of the Chester box on 67 minutes but the opportunity was wasted by Hannah, who blazed the ball high and wide.
Hannah’s delivery was headed away at the far post. Another free kick on the right came when Clay was brought down by Heneghan, who was booked for the foul.
Brown picked Neilson out from the flag but the winger half-volleyed over the bar. Parslow did well to block a shot from substitute Hall at the other end, before Town won a corner through Hannah on the right.
John-Lewis replaced Oates with 16 minutes to go and he was almost on the scoresheet within a minute, as a volley from 20 yards was deflected over the bar for a corner.
A Chester penalty shout came on 77 minutes for a perceived handball against Pearson but the referee waved play on.
McLaughlin replaced Neilson for the last 13 minutes of the game, with the Mariners still dominating.
Riley could have pulled a goal back for Chester with eight minutes to go when the ball dropped for him 12 yards out but McKeown made himself big and raced off his line to block the shot.
A cross from Mackreth towards the far post had to be headed behind for a corner, which was headed away by Harrison.
Arnold came on in place of Hannah in the Grimsby attack for the remainder of the game, before a foul by Parslow gave Chester a free kick but it was hammered high and wide by Rooney.
Arnold hit a shot just past the near post as the hosts kept looking to add to their score.
And in the second minute of added time, that third goal came when Brown found Mackreth on the left and he pulled it back for ARNOLD to slot home.
It could have been 4-0 soon afterwards but a shot from John-Lewis was blocked by Worsnop.
That proved to be the last chance of the game, leaving Town with three goals, three points and a clean sheet from a highly satisfactory afternoon.
The Mariners are at home again on Tuesday, when Southport are the visitors to Blundell Park.
Check out Nathan Arnold's goal below.