Tyler Toffoli scored the lone goal for the Sharks (27-25-4), who have lost five straight (0-4-1). Yaroslav Askarov made 25 saves.
"Just play more on the inside. The way we scored the goal is the way we need to play," San Jose coach Ryan Warsofsky said.
It was the first game for each team following the break for the Olympic Winter Games Milano Cortina 2026.
Toffoli put the Sharks up 1-0 at 1:17 of the second period, tipping Mario Ferraro's point pass over Wolf's glove from the slot.
Kadri tied it 1-1 at 15:02, burying a wrist shot from the slot over Askarov's glove off a saucer pass from Joel Farabee.
Zary gave Calgary a 2-1 lead at 5:22 of the third period when he collected a pass from Backlund and beat Askarov with a wrist shot to the blocker side from the top of the left face-off circle.
"I just saw a quick transition. It was at the end of my shift, but I saw an odd-man rush and decided to jump in," Zary said.