A first half goal from Nathan Tyson and two second half goals from Dean Furman and Kyle Bennett secured the win for men in red and white.
Terry Skiverton was forced into making one change from the midweek trip to Crewe. Skipper Joe Edwards limped off at half-time at Gresty Road with a ankle injury was forced to sit out the trip to the Keepmoat Stadium. Edwards was replaced by James Berrett in the centre of midfield.
After a comfortable start by the Glovers Ugwu twice found himself behind the Rovers defence only to be denied a shot both times by towering centre back Jamie McCombe.
With just over 20 minutes on the clock, Krysiak made a great save to deny a 25-yard thunderbolt from Paul Keegan, but from the resulting corner the home side opened the scoring.
After initially clearing the corner, midfielder Harry Forrester picked the ball up in the area to fire a shot at goal which was palmed out by Krysiak and Tyson was the quickest to react to prod the loose ball home from six-yards out.
On the half hour mark the home side thought they had doubled their lead. A Kyle Bennett free kick from 25-yards out took a huge deflection off the wall and was heading goal bound, only for Krysiak, who was wrong footed managed to tip the ball wide for a corner.
Town were dealt another injury blow with ten minutes of the first half remaining when Leitch-Smith hobbled off to be replaced by Sam Hoskins.
With the fourth official signalling three minutes to be added on, Town had their best chance of the first half. Neat build up from the midfield saw Ugwu find Shephard on the right. The Swansea City loanee returned the pass to Ugwu, but his shot was well blocked by McCombe.
From the resulting Foley corner the ball was half cleared by the Rovers defence. The ball fell to Berrett, whose volley took two deflections and ended up in the thankful hands of Bywater.
The home side doubled their advantage just before the hour mark when Furman latched onto a through ball from substitute Main to finish past Krysiak from 12 yards.
With just under 15 minutes remaining Town forced a corner on the right. Folley swung the corner in, which was flicked on by Arthurworrey into the path of Moore. The striker turned defender controlled the ball and shot towards goal, but Furman did well to block his shot on the line.
The hosts broke away from the block through Tyson, who looked up to cross the ball across the penalty area into the path of Bennett, who made no mistake from close range.