Dan Boyle scored a pair of power-play goals for the Sharks, but he couldn't beat Ondrej Pavelec in the shootout. Pavelec stopped Logan Couture, Tommy Wingels and Boyle as Ladd scored the lone goal in the penalty-shot contest.
Tomas Hertl and Wingels added goals for the Sharks (10-2-5), who lost in a shootout for the third time in their last four games.
The Sharks took a 4-3 lead early in the third period on a precise play, with Couture's no-look, backhand pass setting up Boyle for an easy goal from point-blank range.
Patrick Marleau appeared to have scored the overtime winner for San Jose, but the goal was disallowed when Wingels made contact in the crease with Pavelec.
Niemi stopped 42 of 46 shots for the Sharks, while Pavelec made 30 saves for Winnipeg.
The Jets have won back-to-back contests for the first time since the season's first two games.
The Sharks took a two-goal lead into the first intermission despite being badly outplayed for much of the opening period. The Jets, who scored four first-period goals against Nashville on Friday night, were buzzing around Niemi early, but the netminder kept the game scoreless.
Winnipeg had a 10-2 lead in shots when Boyle's point shot on the power play opened the scoring for San Jose at 14:04. Less than two minutes later, Jason Demers sprung Hertl on a breakaway with an 80-foot pass, and Hertl beat Pavelec with a deke to his forehand for his 10th goal of the season.
The Jets drew even in the second period, beating Niemi three times on 17 shots. Frolik scored off a perfect cross-crease pass from Matt Halischuk to make it 2-1, only to see the Sharks restore their two-goal lead 41 seconds later on a high shot from in tight by Wingels.
Byfuglien scored his first goal of the season - on his 64th shot on goal - to make it 3-2, and Clitsome drew the Jets even with a wrist shot through traffic from 50 feet out.
Notes: A pre-game moment of silence was observed for Remembrance Day, and Second World War veteran Len Kropioski, a Jets season-ticket holder, joined anthem singer Stacey Nattrass on the ice. … The Jets' struggles on the power play continued as they went 0-for-2. Winnipeg has one power-play goal in its last 14 games. … San Jose plays its next three games in Western Canada before a trip to Chicago next weekend. … Winnipeg plays in Detroit Tuesday night before returning home to face Philadelphia.