The Robins earned all three points in Mark Cooper’s 100th League game in charge and had to overcome Andy Williams’s missed first half penalty before Hylton popped up to score the only goal of the match.
Mark Cooper made three changes to his starting line up with Harry Toffolo, Anton Rodgers and Jon Obika starting in place of Raphael Rossi-Branco (suspended), Yaser Kasim (suspended) and Michael Smith (tactical)
The visitors kicked off playing towards the Town End but it was the Robins who had the first attack of the match when Andy Williams picked up possession in midfield and he advanced before firing in a shot just wide of the goal.
The visitors responded with a corner which saw Luke James flick over from close range in the 7th minute and two minutes later, Jordan Turnbull was penalised for a challenge near the angle of the penalty area and was shown a yellow card before Maddison fired over from the free kick.
Swindon responded with some patient build up play before Ben Gladwin’s wayward pass ended the move.
Town earned a corner in the 16th minute when Ricketts attempted pass to Williams was knocked behind by a defender but the resulting cross was caught by the keeper.
Ben Gladwin fired in a decent shot from midfield in the 21st minute but the ball went narrowly over the crossbar with the keeper scrambling across his line.
Harry Toffolo was shown yellow in the 23rd minute for a late challenge on Jack Payne who needed treatment momentarily before rejoining play.
Jordan Turnbull threatened with a glancing header in the 28th minute from a cross by Byrne but the Peterborough keeper Ben Alnwick dived to his left and caught the ball.
Town were awarded a penalty in the 29th minute when Obika was floored in the area by Michael Smith who was cautioned for the foul before Andy Williams’s effort struck the crossbar and rebounded to safety.
Ben Gladwin went close to opening the scoring in the 33rd minute after latching onto a loose ball in midfield before firing in a vicious shot just wide of goal with the keeper beaten.
Peterborough gained a corner in the 36th minute when a cross was deflected behind and Foderingham chose to punch the cross away which led to a first time shot saved by the keeper with his knees and Kgosi Ntkhe’s first time effort went wide from the rebound. Foderingham needed treatment for a knock but was able to continue after treatment.
Luongo tried his luck from 20 yards or so with a dipping shot which went over the bar in the 40th minute.
Ben Gladwin continued to show his attacking intent with a dipping shot which the keeper did well to tip over for a corner and when that was taken, Anton Rodgers tried an audacious shot on the turn from midfield but his effort flew over the bar.
Town had two corners in added time thanks to Luongo’s efforts but they were unable to get a clear shot on goal before the half time whistle was blown.
The second half started off scrappily for the Robins with some misplaced passes putting the defence under pressure and Posh were denied a certain goal when Foderingham pushed away Maddison’s shot from close range at the expense of a corner.
Andy Williams wasted a glorious opportunity in the 52nd minute when Byrne’s superb cross evaded everyone and when the ball reached Williams, he could only divert the ball wide of goal with his knees with the goal at his mercy.
The visitors were looking more attack minded as the half wore on and Luke James tried his luck from the edge of the area but the ball went wide of the upright in the 57th minute.
Jack Payne tested Foderingham with a rasping shot from 30 yards but the Town keeper did well to push the ball away and the Town defence cleared the danger.
The visitors had two corners in quick succession with Town unable to get out of their own half but eventually the danger was cleared. John Swift replaced Anton Rodgers during a break in play in the 64th minute.
Town were awarded a free kick on the left wing in the 68th minute when Toffolo was hacked down but Gladwin’s curled free kick flew over the bar.
Andy Williams was replaced in the 69th minute by Jermaine Hylton who made a superb impact when he latched onto Jon Obika’s pass and his first time shot evaded the keeper and the ball went into the left hand side of the goal to give Town the lead in the 71st minute.
Maddison was replaced by Erhun Oztumer in the 75th minute and shortly afterwards Conor Washington fired in a powerful shot that was parried by Foderingham.
Peterborough continued to press hard for an equaliser but the Town defence stood firm and eventually a superb counterattack started by Swift saw Byrne send in a superb shot which the keeper did well to push way for a corner and when that was taken, Toffolo also fired in a powerful shot which the keeper saved.
Jon Obika left the field to good applause when he was substituted by Michael Smith in the 86th minute.
Massimo Luongo did well to kick the ball away from James who was poised to shoot from close range in the 88th minute.
Peterborough replaced Payne with Harry Beautyman as the match entered the 90th minute.
The main threat to the Town goal in the three minutes of added time came from a corner by Posh which saw their goalkeeper join the attack but the ball was headed away before a free kick was awarded to the Robins for a push.
The final whistle was blown with Foderingham in possession of the ball and Town now move onto 73 points from 40 matches and remain in 3rd place.