John Tavares had a goal and two assists, Josh Bailey added a goal and an assist, and Andrew Ladd also scored to help the Islanders win for the third time in four games. Thomas Greiss stopped 28 shots.
Ladd's goal at 3:12 of the third period broke a 2-2 tie. Rookie Mathew Barzal created the scoring chance by taking the puck around the net and then setting up Ladd in the high slot for his second of the season.
Lee's second of the game and fifth of the season gave the Islanders a two-goal cushion with 8:13 remaining as he converted an odd-man rush.
Tavares sealed the win with an empty-netter with 55.4 seconds remaining and helped improve to 22-4-4 in their two-plus seasons at Barclays Center. Tavares points were his first since he had two goals and an assist Oct. 7 against Buffalo, ending a five-game drought.
The Sharks scored the game's opening goal at 6:26 of the second period on the power play. San Jose came away with the offensive draw and Couture scored from the slot, redirected Brent Burns' point shot past Greiss.
The lead lasted just over a minute as Nick Leddy worked his way to the back of the net and then quickly fed Lee for the tying goal.
The Islanders went ahead 58 seconds later after Joe Thornton made a costly turnover in his own end to give Bailey a point-blank chance. Bailey was able to sneak the puck with a backhander between his skates and past Dell to put New York ahead 2-1.
However, an impressive effort by Jannik Hansen to spin past Brock Nelson in the neutral zone led to a quick feed to Couture, who took a few strides and then fired a shot past Greiss to even the score once again.
The Islanders held a special pregame ceremony to honor alumni of the organization who were in town for an Islanders Alumni Weekend. Among the players on the ice were Bobby Nystrom, Clark Gillies, Bryan Trottier and Ed Westfall. ... The Islanders scratched D Scott Mayfield, F Josh Ho-Sang and F Nikulay Kulemin. ... San Jose scratched F Joel Ward, F Barclay Goodrow and D Dylan Demelo. ... The Islanders honored Tragically Hip front man Gord Downie by playing music from the band during warmups. Downie passed away on Oct. 17 after succumbing to brain cancer.
Sharks: At the New York Rangers on Monday night.
Islanders: Host Arizona on Tuesday night.