Calgary went into the night's action trailing Detroit by one point for the last playoff berth in the Western Conference.
San Jose lost its fifth straight and remained tied with idle Chicago atop the conference with 96 points.
Calgary built a 4-1 lead, with Eric Nystrom finishing off the surge by scoring on a wrist shot with 8:57 remaining in the second period.
Miikka Kiprusoff then gave up third-period goals to Manny Malhotra and Dan Boyle that allowed San Jose to get back into the contest. Boyle's goal came with 1:51 remaining, but Kiprusoff fought off a flurry of shots at the end and finished with 25 saves.
Evgeni Nobokov took the loss, giving up all four goals on 24 shots.