The first half, territorially, belonged exclusively to Wycombe. The home side dominated possession, but couldn't find the key to unlock the resolute Cobblers defence.
Nathan Tyson, the Chairboys striker recently the subject of an unsuccessful bid by Luton Town, got away on the left in the third minute but his pull-back bisected his two onrushing colleagues.
Matt Bloomfield latched onto an Ian Stonebridge throughball six minutes later but his shot was well saved by Lee Harper.
Wycombe's best chance of the first period came just before the half-hour mark. The lightening quick Tyson latched onto a throw from keeper Frank Talia, beat two defenders, but saw his blistering shot beaten away by Harper.
The sucker punch from the visitors came right on half time. Ex-Colchester hit man McGleish latched onto a ball misjudged by home defenders Roger Johnson and Stuart Nethercott and his 20-yard effort sailed over the helpless Talia.
It could have been worse for Wycombe just a minute later when Lee Williamson took aim from 20 yards, but his left-foot effort sailed just wide.
The home side did have the ball in the Cobblers net on the hour mark, but as Tyson turned away to celebrate the equaliser an offside flag stopped him in his tracks.
Johnson was also flagged offside seven minutes later before he too smashed a shot past Harper, but Northampton held on to record a valuable away win.