His 79th-minute strike also dumped the Cobblers into the bottom four.
In a match which could have produced a lot more goals, Yeovil had the better chances early on.
When Nathan Smith burst through in the 12th minute, his thunderbolt shot crashed into the body of goalkeeper Chris Dunn.
Mark Hughes completed the clearance by conceding a corner and, from the set-piece, another goal-bound Yeovil shot, this time by Obika, was blocked on the line by man-of-the-match Danny Jackman.
Yeovil had plenty of defending to do but goalkeeper Chris Weale - who kept his third successive clean sheet since moving back to his old club on loan from Bristol City - made several timely saves.
On one occasion Jackman provided an opening for top scorer Adebayo Akinfenwa, but his header flashed just wide.
Obika and Gary Roberts went close for Yeovil in the opening minutes of the second half but it was not until the 79th minute that Obika won the game.
He was cleverly put through by substitute Luke Rodgers and goalkeeper Dunn had no chance.
Four minutes later Dunn should have been beaten again but Andy Welsh shot against his legs when clean through. In a dramatic finale Jackman hit a post for Yeovil and the ball rebounded kindly into the arms of Weale.
Northampton had one further chance deep in to stoppage time but Yeovil managed to keep a third successive clean sheet and seven points from the last nine has taken them clear of immediate trouble.