Louis Crevier scored twice, Connor Bedard had two assists, and Spencer Knight made 15 saves for the Blackhawks (29-39-14), who had lost nine of 10 (1-8-1) entering their final game of the season.
Mario Ferraro and Michael Misa each scored, Kiefer Sherwood tallied two assists, and Yaroslav Askarov made 19 saves for the Sharks (38-35-8), who will finish their season at Winnipeg on Thursday.
Ferraro put the Sharks ahead 1-0 at 8:09 of the first period. He got the cross-ice feed from Sherwood on the rush and his wrist shot from the right face-off circle deflected off Blackhawks defenseman Ethan Del Mastro’s skate and into the net.
The Blackhawks’ Ilya Mikheyev was stopped on a penalty shot at 16:22, shortly after getting the team’s first shot on goal at 15:50.
Just 43 seconds into the second period, Toffoli looked to put the Sharks up 2-0 but the play was challenged and successfully overturned for offside.
Misa gave the Sharks a 2-0 lead with a power-play goal at 5:17. Misa worked the puck along the goal line and attempted to put it in front, with the puck again deflecting off of Del Mastro in front and sliding over the goal line.
The Blackhawks five-goal rally started with Sam Rinzel, who brought the Blackhawks to within 2-1 at 19:30. Ryan Donato skated the puck down the center and lost it, with Rinzel jumping on the puck and putting it through Askarov's five-hole.
Crevier tied the game 2-2 at 3:51 of the third period. Bedard picked up the puck in the defensive zone and carried it up the ice, making a backhand pass to Crevier, who snapped it into the net.
Greene scored the go-ahead goal at 8:35 to give the Blackhawks their first lead of the night. He took a backdoor pass from Del Mastro and scored from the left side of the crease.
Crevier scored again at 10:32 to make it 4-2. Tyler Bertuzzi got the puck off the boards and set Crevier up for the one-timer from the right point.
Nick Lardis made it 5-2 at 14:44 after taking a pass in the slot from Bedard and dropping to one knee to put a wrist shot over Askarov stick side. With the assist, Bedard reached 45 helpers on the season, surpassing his career best of 44 set last season.
