McGowan's sensational strike was the difference at half-time before Mitch Pinnock added a sweet second just four minutes after the restart.
Town were coasting to victory when former Cobblers midfielder Chris Lines pulled one back with nine minutes to play, but that came too late to stop YTown picking up three vital points, which keep them second in a very tight Sky Bet League Two table.
A knee injury to Shaun McWilliams forced Jon Brady into one change against Stevenage as Bez Lubala came in and Paul Lewis retreated into a central midfield role.
Both sides had moments of promise but, bar Pinnock's blocked shot, there was little to worry either goalkeeper in a scratchy opening 15 minutes.
But there was nothing wrong with McGowan's stunning opening goal just three minutes later. Louis Appere flicked on a left-wing cross and the fast-arriving McGowan unleashed a sweet half-volley which whistled into the far bottom corner.
Sam Hoskins followed McGowan's lead and had a go himself, his shot well blocked, before Town lost their other full-back, Ali Koiki, to injury, with Joseph Mills brought on in his place.
Northampton were comfortable in the opening half-hour but they came under increasing pressure as half-time neared and Stevenage did create one clear opportunity to equalise, however Elliot List fluffed his lines after being sent through on goal.
Cobblers needed a second goal and they got it just four minutes into the second-half when Lewis' cross was only cleared as far as Pinnock, he took a couple of touched before firing powerfully past Posh loanee Christy Pym.
That took the wind out of Stevenage's sails and they struggled to muster a response, with Town close to a third through Jack Sowerby's long-range shot that had to be beaten away by Pym.
Jon Guthrie's header was also straight at Pym while ex-Town man Lines nodded over in a rare chance for Stevenage.
Despite the home side's lack of threat, though, they set up a nervy finish with nine minutes to play when a well-worked move down the right resulted in Lines sliding home.
There were to be no major scares in what time remained, however, and really the Cobblers should have made their victory more secure with Chanka Zimba missing two excellent chances to kill the game off in the final few moments.
Stevenage: Pym, James-Wildin, Prosser, Upson (Read 56), Vancooten, O'Neill, Taylor, Lines, Carter, Norris (Westbrooke 45), List
Subs not used: Walker, Reid, Barry, Tinubu, Clements
Cobblers: Roberts, McGowan, Horsfall (c), Guthrie, Koiki (Mills 26), Sowerby, Lewis, Lubala (Rose 72), Pinnock, Hoskins, Appere (Zimba 61)
Subs not used: Maxted, Harriman, Magloire, Ashley-Seal
Referee: Craig Hicks
Cobblers fans: 568