In front of a buzzing home crowd, Brentford, who had won three games in succession, started confidently and, although their neat passing strategy didn't punch any holes in Town's defence, the signs looked promising.
But the Cobblers looked dangerous on the break and should have made the most of decent deliveries from wide areas.
Northampton were unlucky not take the lead with a shot conjured up out of nothing, when Jordan Robertson unleashed a right-footed shot that cannoned off Brentford's crossbar.
As Northampton cranked up the pressure, Bees keeper Nathan Abbey was then forced to stop a downward header from Kenny Deuchar from point-blank range.
Northampton finally made the breakthrough just after the half-hour mark in spectacular fashion. Former Brentford loan recruit Crowe poured misery on his old club by sending a 30-yard screamer into the roof of the net.
The visitors thoroughly deserved to take the lead and, as a result, their confidence grew collectively with the side linking up well to cause Brentford endless problems.
Brentford's only genuine chance of the first half arrived via a set-piece when skipper Kevin O'Connor connected with Joe Keith's corner, only to see his header flash wide of the target.
Just before half-time Northampton were only prevented from doubling their lead thanks to a miraculous double save by Abbey, who somehow managed to block Robertson's close range effort.
After the break, the visitors remained comfortably in control and carved out a couple of decent chances and Andy Holt came closest to extending his side's advantage.
But Brentford refused to buckle and staged a remarkable comeback. After chalking up a succession of corners, the home side repeatedly probed Northampton's back-line and seasoned campaigner Neil Shipperley almost equalised.
But the ex-Crystal Palace target man's header was palmed away by Town keeper Mark Bunn and then Bees youngster Charlie Ide had a half-volleyed effort stopped by the visitors' custodian.
In a last-ditch bid to find an equaliser, Brentford boss Scott Fitzgerald introduced striker Calum Willock and the substitute's pace almost found a way through.
But Northampton kept both their nerve and concentration and managed to clear their lines with comfortable efficiency and clung on to record a crucial victory.