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In an entertaining contest played in bitterly cold and windy conitions, the Mariners took the lead from the penalty spot as Thomas scored his first of the game.
Their lead was to last just two minutes though, as a superb Matt Taylor free kick brought the visitors level.
Swindon had the better of the early stages of the second half but Town got themselves back in front when Thomas made it 2-1 just after the hour.
And the hosts held firm under pressure from their visitors to collect an important three points.