Akinfenwa should have done better with an early header while at the other end John O'Flynn shot wide following good work from Arron Davies and Craig Woodman.
Top scorer Jamie Cureton was denied by Langmead after he pounced following a good save from Lee Nicholls. But Akinfenwa broke the deadlock in the 25th minute when he controlled a cross from Chris Hackett on the edge of the box before turning and volleying home.
Cobblers doubled their advantage in the 39th minute when on-loan midfielder Emyr Huws beat Kevin Amankwaah and O'Flynn before crossing for skipper Langmead to grab his third goal of the campaign.
Either side of the break, Davies missed a great chance and after the restart Cureton's smart volley was well saved by Lee Nicholls. Cobblers also had chances, Akinfenwa almost grabbed his second when he headed over and Alex Nicholls flashed a shot just wide. It took a super save from Lee Nicholls to prevent Cureton from pulling a goal back late on following a much better second half from City.
But Alex Nicholls made sure of all three points in the 84th minute when he headed home after Langmead had helped on Hackett's free-kick.