The Cobblers' leading marksman took his season's tally to 14 as the Nationwide Conference side saw their tilt for glory fade with a disappointing whimper.
But there was almost a sting in the tail for McGleish, who became one of seven first-half bookings from referee Darren Deadman for an ill-advised celebration in the net after his opener, a 43rd minute tap in after Alan Julian had parried Martin Smith's rasping drive.
There was some ill feeling between the sides after the 2-2 draw at Broadhall Way and Stevenage were forced to use some strong arm tactics in the first 45 minutes.
They tried to stem the home side but there was bookings to Robert Quinn, Michael Brough, Dannie Bulman and Ollie Berquez for the visitors as well as Luke Chambers, Pedj Bojic and McGleish for Northampton.
McGleish virtually sealed the tie in the final minute of the first half when Smith was allowed to find him unmarked just a few yards from goal and he headed the ball into an unguarded net.
In truth, Northampton should already have been ahead and it had taken some desperate defensive scrambles as Stevenage kept their goal in tact.
Barry Laker deflected a fierce Josh Low drive before heading towards his own goal and forcing Julian to push the ball on to the roof of the net.
Stevenage didn't muster a serious chance until the 79th minute when Jon Nurse glanced a header wide from a Danny Williams cross before cutting in and driving a low shot across goal soon after.
But the last word could have rested with McGleish when he was denied a hat-trick eight minutes from time with Julian pushing away his effort.