Grimsby Town slipped to defeat on their first-ever visit to Salford City's Peninsula Stadium.
he Mariners lost by a single goal, scored by midfielder Mark Shelton from a first-half free kick.
Town thought they had got themselves back on level terms when Cook found the net from a free kick four minutes after the break but the celebrations of the travelling fans were short-lived as goal was ruled out.
Afterwards, the visitors kept pushing for an equaliser but it was not to come, with Luke Waterfall denied by a magnificent save in the dying moments of the contest as Salford held on.
Matt Green returned from illness to face his previous club in one of two changes to the Town side that drew with Oldham on Saturday, with Jordan Cook the other to come back in as Max Wright and Elliott Hewitt dropped to the bench.
James McKeown started in goal, with Luke Hendrie, Ludvig Ohman, Luke Waterfall and Liam Gibson forming the defence.
Cook was joined in midfield by Jake Hessenthler and Elliott Whitehouse, with James Hanson and Moses Ogbu alongside Green in attack.
The Grimsby substitutes were Sam Russell, Ethan Robson, Harry Clifton, Charles Vernam, Matty Pollock, Hewitt and Wright.
Salford manager Graham Alexander made eight changes as his side looked to bounce back from a home defeat by Cheltenham Town on Saturday.
They would look to the likes of striker Adam Rooney to fire them towards a second league win of the season, while there was a familiar name on the home bench in the shape of former Town loanee Nathan Pond.
An early cross from Ibou Touray on the home left was headed clear, before Town's first chance saw Green meet a cross from Gibson but his header was tipped over the bar by keeper Kyle Letheren.
A Hessenthaler free kick on seven minutes was met by Waterfall on the edge of the penalty area before being cleared.
Another opening came two minutes later when Hanson foun some space on the right but when the ball broke for Cook, he could only shoot tamely wide from 20 yards.
Green fired wide from a similar distance on the right, then Rooney headed over the bar at the other end after a cross had been helped on by Mani Dieseruvwe.
Town won a corner on the left when a Gibson cross was cut out but the ball was eventually cleared after Hssenthaler's delivery from the flag.
But when the first goal came on 21 minutes, it was Salford who took the lead. A foul by Hanson gave the hosts a free kick 25 yards out and SHELTON'S swerving shot from it beat McKeown.
The Mariners' response was good as Hanson won a corrner but they were unable to make it count.
Cook was shown the first yellow card of the night for a foul on Dieseruvwe, then a foul on Whitehouse gave the visitor another oportunity to put the ball into the box. Hessenthaler's free kick was headed away as far as Cook but his volley from 20 yards was blocked.
The home side went close when Touray ran down the left and shot from the edge of the box but his low effort flashed wide of the far post.
After a reasonably bright opening by the Mariners, Salford had taken control of the game as the half went on and were looking solid at the back and the more dangerous of the two sides in attack.
Town were having some good spells of possession though and another came around the 40-minute mark, although the final ball proved too high for Hanson and went out for a goal kick.
Ohman was forced off with an injury as the game moved into stoppage time, with Hewitt coming on in his place.
No further chances came before the half-time whistle, meaning the hosts kept their advantage going into the dressing rooms and Town would have to improve after the break if they were to get anything from the game.
The Mariners began the second half brightly, seeing plenty of the ball in the Salford half and forcing an early corner, which was cleared.
A foul on Hanson brought a free kick in a central position four minutes in and from it, the Mariners thought they were level as Cook stepped up and fired past Letheren into the net in front of the travelling supporters.
But their joy was short-lived as after consulting with the fourth official, the referee ruled the goal out and gave a free kick to the home side after Hessenthaler was stood too close to the Salford wall.
Lois Maynard sent a wild shot well over the bar from 25 yards after the ball had broken to him, before Dieseruvwe's header from a right-wing cross was deflected through to McKeown.
Hewitt did well to win a corner on the Grimsby right on 62 minutes but Hessenthaler's ball from it was headed away at the near post.
Another corner came soon afterwards as the pressure continued to build, with another one quickly following on the left but again, Town were unable to make it count.
A foul by Waterfall gave Salford a free kick on 66 minutes and from it, they went close to doubling their advantage but luckily for the away side, Cameron Burgess' header dropped wide.
Green saw a shot well blocked at the other end after good work by Hewitt down the right, before Hessenthhaler thought he had won a corner after his shot appeared to have taken a deflection but instead, a goal kick was given.
A corner came at the other end soon afterwards and it led to two shots being blocked in quick succession as Town's deficit remained at one goal.
Robson replaced Whitehouse on 73 minutes, before a cross from Touray was headed down to McKeown.
The final Grimsby change saw Vernam replace Cook with 14 minutes left to play but it was Salford who created the next chance, as a quick counter-attack led to midfielder Danny Whitehead shooting from the edge of the box. Hewitt was in the right place to make a good block.
Luke Armstrong replaced Whitehead on 83 minutes before Green won a corner on the Town left, although Robson's delivery was headed away.
Pond was sent on in place of Rooney for Salford for the last three minutes and the Mariners were given an additional four minutes to search for an equaliser.
They almost had it when Waterfall hit a shot that looked destined for the top corner of the net but having had little to do all evening, Letheren somehow got fingertips to the ball to tip it over the bar.
Town kept pushing for a leveller but it was not to come as Salford held on for all three points.
The Mariners are next in action on Saturday, when they host Macclesfield Town at Blundell Park.
Salford: Kyle Letheren, Sam Hughes, Cameron Burgess, Carl Piergianni, Scott Wiseman, Ibou Touray, Mark Shelton, Lois Maynard, Danny Whitehead, Adam Rooney (C), Emmanuel Dieseruvwe.
Subs: Ewan McFarlane, Joey Jones, Nathan Pond, Alex Doyle, Danny Lloyd, Luke Armstrong, Devante Rodney.
Town: McKeown (c), Hendrie, Öhman, Waterfall, Gibson, Hessenthaler, Whitehouse, Cook, Hanson, Green, Ogbu
Subs: Russell, Robson, Clifton, Vernam, Wright, Hewitt, Pollock.
Referee: Christopher Sarginson
Possession: Salford City 34% - 66% Town
Corners: Salford City 2 - 9 Town
Next Up: Macclesfield Town (H)