Sharp set up Marian Hossa's tying goal in the final minute of regulation and then got the game-winner 43 seconds into overtime to lift the Blackhawks to a 3-2 win over the Montreal Canadiens on Wednesday night.
Jeremy Morin also scored in the Blackhawks' fourth straight win overall, and their first in overtime this season after seven losses despite leading in the NHL in goal scoring.
"I think we were due," Chicago coach Joel Quenneville said. "We're a pretty good club offensively, but to take this long to get one. ... It's certainly a relief, and a huge two points for us and a nice comeback as well."
Defending Stanley Cup champion Chicago may need some of that late magic when the playoffs start next week.
"It's not the type of overtime you see in the playoffs," Quenneville said, "but going forward, it gets the monkey off our back."
Sharp scored the winner -- and his team-leading 34th goal -- on a shot from the slot that struck Montreal goalie Peter Budaj, rolled high off his equipment, ticked off the left post and landed in the net.
"It was at the end of a shift," Sharp said. "I let go of the shot. Makes up for the ones that hit the post."
Hossa had tipped in Sharp's feed from the right corner left to tie the game at 2 with 47.7 seconds left in the third period.
"Michel Handzus made a great pass to me and I just wanted to get it toward the net," Sharp said. "I saw Hoss' stick and he put it in."
The Blackhawks put on a strong, wild finish to win a cautiously played game between Original Six rivals with depleted lineups.
"I don't think we were especially happy with the way we played the first couple periods, but picked it up there towards the end," Chicago defenseman Duncan Keith said. "Their goalie made some big saves, too."
Dale Weise and Francis Bouillon scored for Montreal, which snapped a two-game win streak and lost for just the third time in its last 13 games. Budaj had 25 saves.
The Canadiens were without starting goalie Carey Price and defensemen Andrei Markov and Alexei Emelin, who didn't make the trip to Chicago so they could rest for the playoffs. Montreal will face Tampa Bay in the opening round, with home ice to be determines.
"I thought we played a solid game," Montreal coach Michel Therrien said. "On the last two goals, it was some bad coverage in front of the net.
"I'm sure on the last goal, the winning goal, Peter certainly would like to see that shot again, but those things happen. This is not an easy place to play, but our effort was there again."
Chicago's played its fourth game without star forwards Jonathan Toews and Patrick Kane. Both are expected to miss the remainder of the regular season, but return for the playoffs.
Earlier on Wednesday, Kane said he will be at 100 percent for the postseason despite a brace on his injured left knee.
Kane, who was leading Chicago in scoring when he was hurt in a game against St. Louis on March 19, resumed skating on his own five days ago. On Wednesday, he skated with his teammates for the first time in the hours before the game against Montreal.
Canadiens forward Alex Galchenyuk played only two shifts in the first period before suffering a lower-body injury and did not return.
The Canadiens won the other game this season between the teams on Jan. 11 in Montreal.
All the scoring came after the second period.
Weise, who had sat out the last six games with an upper body injury, got the Canadiens on the scoreboard first, completing a 3-on-2 break after taking a feed from Josh Gorges at 7:31 of the third. Gorges was playing for the first time since March 5 after undergoing surgery on his left hand.
Morin tied at 10:34 on a low shot from the right circle that slipped between Budaj's pads.
Bouillon put the Canadiens back ahead just 22 seconds later, as his high screened shot from the point slipped past Crawford's shoulder.