McGleish made it seven goals in his last nine matches, taking his seasonal tally to 13 by popping up with the winner five minutes from time when he crashed a rising shot into the top corner after Josh Low had worked his way behind the Pilgrims defence.
All three goals came in the final 18 minutes with Northampton grabbing the lead thanks to Martin Smith's left-foot drive. The ball found its way back at Smith's feet after his corner had produced two goal-line clearances, the first a header by Chris Willmott which was nodded away by Danny Thomas.
But Northampton joy went immediately flat when Ashley Westwood's pitiful back pass was seized upon by Boston's leading scorer Andy Kirk, the striker lobbing Lee Harper to square things up.
Kirk immediately cracked a shot against the cross bar while the lively Thomas was just wide in the 83rd minute with a left-foot shot on the turn.
The scene was set for McGleish's moment of magic, but held at contrasted with a forgettable opening hour.
Northampton struggled to break down the visitors defence and almost fell behind in first half injury time with what would have been a comic own goal from Fred Murray when he headed an Austin McCann free-kick back over his goalkeepers head, only for Chris Willmott to hack the ball clear.
The only save of significance until the closing stages was an early strike by Eric Sabin which forced former Northampton goalkeeper Nathan Abbey into a sharp save.
Northampton's frustration intensified as the second half went on and Boston almost punished them in the 68th minute when a McCann free kick was met by the head of Paul Ellender whose goal attempt was deflected narrowly wide.