Two gift goals sent Swansea slipping to defeat but they did enough to suggest that better times are ahead for Kenny Jackett's side.
A poor defensive header let the visitors in for an early opener and debutant Sam Ricketts headed into his own net in the closing minutes.
City started with four players making their debuts while the Cobblers had new boy Scott McGleish up front, partnering former Swan Marc Richards.
The visitors took the lead in the third minute - a Stuart Jones back pass failed to reach Willy Gueret in the home goal. Richards toe-poked against the post and McGleish was on hand to tap in the rebound.
Four minutes later Roberto Martinez slipped a through ball in for Paul Connor who was brought down inside the area by Northampton skipper Christopher Willmott. To everyone's amazement referee Mike Fletcher waved play on and Northampton raced down to the other end and Jones was forced to clear off the line from Bertrand Cozic.
Kristian O'Leary fired in a shot that stunned Lee Harper's fingers as the Swans tried desperately get back on level terms, then it was Andy Robinson's turn to drive one in at the near post but Harper dived to palm away for a fruitless corner.
As the first half drew to a close, Alan Tate flashed a header goalwards from a Robinson corner, but David Galbraith hacked it off the line.
Dennis Oli came on for the ineffective Adrian Forbes just after the hour and his presence opened up a gap for Connor, but the former Rochdale striker shot tamely at Harper.
In the 68th minute Oli was brought down on the edge of the area, but Harper leapt high to clutch Robinson's free-kick.
The visitors made the points safe in the 83rd minute when a cross from the impressive Galbraith was headed into his own net by Ricketts under pressure from McGleish.
Kenny Jackett dispointed with the result because "I was determined to eradicate the letting in of silly goals that is exactly what happended today. It was a poor start to concede a goal from a mistake and another error costs us towards of the game. it was very fustrating to see my players give up after that second goal and that is something i will not tolerate. We did put them under alot of pressure during the game but didn't get behind them as much as i would like".
Colin Calderwood "It's just one day but if we had thirty days like this then it will be very handy. The first day of the season always have so much importance placed on it but whatever the result all you are hoping for is to see within the team the way you want the game to be played together with a bit of spirit".
"If that is their then there is something to take on. Their is an eagerness within the squad to win the promotion and get sucess on their CVs".
"Swansea gave us a stern test defensively and we were certainly stretched at times and whoever come to the Vetch will need to stand up and be counted".