Pavelski and Joonas Donskoi scored in the shootout, when Jones denied Sean Monahan and Mikael Backlund.
The Flames were 10-0-0 when leading entering the third period.
"After they tied it at 2, they grabbed some momentum," Flames captain Mark Giordano said. "Again, shootouts are tough. During OT, we had one go off the cage. It's disappointing especially since they are ahead of us in the standings. For them to get that extra point hurts.
"It feels like these shootouts we've been on the wrong end of it. I think they got the momentum on that first shootout goal, and it gives you a big advantage."
Pavelski scored in the first period for the Sharks (20-11-4), who have won three games in a row and are 4-1-1 in their past six, all within the Pacific Division.
"Critical points, especially with [Logan] Couture out of the lineup," San Jose coach Peter DeBoer said of the center who has missed four games with a concussion. "We talked about that, the ability to put teams in holes behind you as opposed to let them close the gap on you. We all know how important the last 40 games are. We know some of these teams are going to go on runs. You want to build as much of a cushion as you can."
Garnet Hathaway and Backlund scored in the first for the Flames (18-15-4), who have lost two games in a row. Rittich made 30 saves in his fourth NHL start of the season.
"He made some crucial saves when we needed him to," Calgary coach Glen Gulutzan said. "He had a solid outing. He was in their faces during the shootout. It's a tough position to be in. Joonas coming down on you is not an easy thing to defend against. We needed to put some goals on the board for him."