They did it on the back of a double strike from highly-rated marksmen Luke Varney, who took his tally to the season to 22 with goals after 26 and 57 minutes.
Northampton were parading their new loan signing from Gretna Kenny Deuchar but, although he made a bright debut in attack, it was Varney who grabbed all the headlines.
The visitors went in front when Ryan Lowe threaded a pass into Varney's path and he finished coolly as goalkeeper Mark Bunn ran from his goal.
Northampton went close in the first half with Deuchar seeing a shot shave a post, while Andy Holt burst into the box two minutes before the break but lashed his effort wide.
The home side were on level terms ten minutes after the restart thanks to the enterprise of Jason Crowe down the right flank. He cut into the box and delivered a fierce cross which was hammered home by Bradley Johnson.
But the relief lasted only two minutes as Darren Moss sent Varney dashing clear and the striker again finished with precision.
Chris Doig was unlucky to see an effort ruled out for offside, while Deuchar had a shot on the turn saved by Ben Williams.
Meanwhile, at the other end, Varney headed on to the roof of the net from a Lowe shot.
Northampton brought on their two on-loan substitutes Marc Laird as Jordan Robertson and both had efforts on the goal, with Laird's flashing header late in the game forcing a save from Williams before the lively Robertson turned sharply in the box but fired over the crossbar.
Northampton have now lost nine times in front of their home fans this season, but this was an encouraging performance from Crewe who had shipped seven goals in their last two matches.