After a windswept opening 45 minutes when the hosts failed to make best use of the conditions at their backs, it was Brighton who stole the initiative, ending a run of four straight draws to leave Dean Wilkins' men on a run of just one defeat in nine matches.
Savage opened the scoring on the hour when he swept home the ball from six yards after Alex Revell had headed a free-kick by Kerry Mayo back across goal into the danger zone.
And the points were virtually wrapped up five minutes later with Revell again involved when he out-jumped goalkeeper Mark Bunn after a cross from Jake Robinson and it was Savage who nodded home from close range.
Brighton could have made the victory even more emphatic in the 72nd minute when Revell cut in from the left and fired a fierce cross-shot which was only blocked by Bunn. The onrushing Robinson somehow managed to crash his effort against the bar from only two yards.
Northampton had come closest in a poor first half with the lively Kenny Deuchar having a shot well saved by Scott Flinders in the sixth minute while strike partner Jordan Robertson lashed a volley high shortly afterwards.
The home side's best move in the opening period saw Bradley Johnson thread a pass to Robertson who went racing clear but Flinders came off his line to save the day with a crunching tackle.
Deuchar blotted his copybook just after the break when he fired wildly over the bar after good work by Simon Cox who made his home debut after coming on at half-time for the injured Robertson. Cox played a neat one-two with Andy Holt but saw his pinpoint delivery wasted by the former Gretna man.
Brighton's more polished football saw them gain the upper-hand and Savage's goals did the rest.