Set up by Patrick Kane's centering pass, Sharp ripped a shot from between the circles past Carey Price to hand the Canadiens' their fifth straight road loss.
Kris Vertseeg and Cam Barker each had a goal and an assist. Barker's power-play goal was only the Blackhawks' second in their last six games.
Cristobal Huet stopped 20 shots in his fourth straight start and beat the Canadiens, one of his former teams, for first time in three games.
Montreal's Mike Cammalleri and Travis Moen scored 4:02 apart late in second period to erase a 2-0 Chicago lead.
Huet played on back-to-back nights for the first time this season. He made 26 saves in a 2-0 loss at Nashville on Thursday night, and has been sharp in his last four starts.
Price made 33 saves in his first start since Oct. 17, a 3-1 loss to Ottawa. Jaroslav Halak had made five straight starts since then, winning the first four before a 6-1 loss at Pittsburgh on Wednesday night.
Blackhawks captain Jonathan Toews missed his fourth straight game because of concussion-like symptoms.
Toews hasn't resumed skating after absorbing a crushing open-ice hit from Vancouver's Willie Mitchell in the third period of a 3-2 loss to the Canucks on Oct. 21. The Chicago star is listed as day-to-day.
Versteeg scored the only goal in the up-tempo first period, with 6:14 remaining. His centering pass from behind the net hit the right skate of Montreal defenseman Marc-Andre Bergeron and deflected past Price.
Chicago's Andrew Ladd knocked Montreal's Matt D'Agostini out of the game with an open-ice hit at the Canadiens' blue line 3:48 into the first. It appeared Ladd slammed D'Agostini in the chin with his shoulder, but referees Stephane Auger and Dan O'Halloran assessed Ladd with an elbowing major and a game misconduct.
Huet made several close-in saves to hold off an extended Montreal flurry midway through the second. Chicago coach Joel Quenneville called a timeout at 9:32 in an attempt to regroup his team.
The move helped.
Montreal's Hal Gill went off for hooking at 9:46. Nine second later, Barker's screened power-play goal from the left circle made it 2-0.
Goals by Cammalleri and Moen late in the second tied it at 2.
Cammalleri cut it to 2-1 with 4:05 left in the period. He beat Huet from the low edge of the right circle after Jaroslav Spacek's shot from the blue line deflected off Chicago's Brian Campbell in front of the net.
Moen took advantage of one of Huet's few lapses to tie with 2.1 seconds left in the period. His wrap-around attempt from right side of the net squeezed in between Huet's left skate and the post.
Huet made a point-blank stop on Guillaume Latendresse midway through the third to maintain the tie.
The Canadiens visited the United Center for ths first time since Oct. 18, 2006, when they lost 2-1. Friday night's game was the only this season between the two "Original Six" rivals. Montreal beat Chicago 4-1 last March in the only 2008-09 game between the teams. … Chicago LW Ben Eager missed his 11th game because of a concussion, but skated earlier in the day for the first time since sustaining the injury. "He skated well," Quenneville said. "It was encouraging today." The Blackhawks don't play again until Thursday night at Phoenix. Quenneville said Toews and Eager will make the trip with the team.