"We're not happy with giving up leads in the third period," Sharp said. "We'd like to close teams out by scoring in the third period and get out of here. But when the games get tight we seem to play better, and that's important.
"It would be a lot worse if we were coming away with no points instead of two."
Corey Crawford stopped Jonathan Huberdeau and Brad Boyes in the shootout as Chicago (6-1-2) scored both goals in the tiebreaker, which ended when Sharp deked Jacob Markstrom before sliding the puck into a half-empty net.
Markstrom came into the game with 2:59 left in regulation after Tim Thomas left with an apparent lower-body injury. Thomas, who finished with 25 saves, was making his third start after missing four games because of a lower-body injury sustained during a 2-1 loss against the Philadelphia Flyers on Oct. 8.
Florida coach Kevin Dineen had no update on Thomas' condition after the game, but said the injury was not the same as the one he sustained in Philadelphia.
After a stoppage of play, Thomas skated over to the Florida bench, flexed his right leg and showed obvious pain, at which time he was pulled in favor of Markstrom.
"I didn't want him to be able to play out there, either maybe hurt himself a little bit more or not be able to play to his full potential," Dineen said.
Crawford made 19 saves in regulation and overtime and stopped Huberdeau on a penalty shot in the second period.
"We had some good goaltending by Corey in the shootout and finally were able to get on the board there," Toews said. "It's nice to win in a shootout when we let a two-goal lead slip like that."
It was the second consecutive shootout game for the Panthers, who beat the Minnesota Wild 2-1 Saturday when Huberdeau and Boyes both scored.
Huberdeau, the reigning Calder Trophy winner, was 2-for-2 on penalty shots last season to go along with a 3-for-5 career mark in shootouts coming into the game. On his penalty shot, he tried to beat Crawford with the same forehand-to-backhand-to-forehand move with which he scored in the shootout against Minnesota, but Crawford never left the right post and made a pad save. Huberdeau tried to beat Crawford between the legs in the shootout, but the goalie got his stick on the puck.
"The first one I came and I think I had him," Huberdeau said. "I just had to go on my backhand. I came back to the same move I did the other night and it didn't work. This one [in the shootout] I tried to go five-hole and it almost worked, but Crawford is a good goalie. I think he read it good."
Toews and Bryan Bickell scored in the second period for the Blackhawks, who haven't scored a third-period goal since their season opener against the Washington Capitals and have been outscored 8-3 on the season.
Patrick Kane had a breakaway in overtime for the Blackhawks but missed the net with a backhand after a deke.
"I was a little frustrated for a second, but there was nothing we could do about it," Crawford said of the Blackhawks squandering their 2-0 lead. "We just moved on. We had some chances in overtime. I think we were able to brush that off pretty easy."
Tomas Fleischmann and Dmitry Kulikov scored in the third period for the Panthers (3-6-1), who missed a chance for their first winning streak of the season. Rookie Aleksander Barkov assisted on Fleischmann's goal, giving him seven points in 10 games.
The Blackhawks have won the last four meetings between the teams, dating back to the 2010-11 season.
Florida trailed 2-0 when Fleischmann one-timed a centering feed from Barkov, the second pick in the 2013 NHL draft, past Crawford at 9:04 of the third. Kulikov tied the score at 11:51 off a defensive zone turnover by Duncan Keith. He intercepted Keith's diagonal pass above the left circle, skated in and beat Crawford to the glove side with a wrist shot.
"I thought it was encouraging that we got two points out of the game," Chicago coach Joel Quenneville said. "It was 2-0 and then it was 2-2 and there was a lot of time left. We stabilized the game at that point and found a way to get two at the end. We're having trouble scoring in the third period.
"I don't think we're playing any different than the first two periods. I don't think we're sitting on leads. We're not complaining, let's put it that way."
Toews opened the scoring at 5:18 of the second period with a power-play goal when he ended a pretty three-way passing play with Kane and Keith. Bickell made it 2-0 at 16:49 when he beat Thomas with a wrist shot from the left circle. Bickell's initial shot was blocked by Kulikov, but the puck came right back to Bickell, whose second shot went over Thomas' glove.
It was the second consecutive game with a goal for Bickell, who was shut out in Chicago's first seven games.
"It was nice to see it go in and maybe he's more comfortable with the puck and hopefully can keep production with that group," Quenneville said. "That line (Bickell, Marcus Kruger, Andrew Shaw) was effective for us tonight."
The teams played a scoreless first period that was pretty even despite Chicago's 12-6 shot advantage. Huberdeau had another good scoring opportunity in that period after some nice stickhandling allowed him to get off a shot from the slot, but Crawford came up with a pad save.
Florida had 14 blocked shots spread among nine players in the opening period.
"I liked the overall effort tonight," Dineen said. "We pushed hard. We had a little trouble finding our range. We were spraying [shots] all over the place. We need to hit the net. But I liked the way we pushed when the score was even, when we got down a couple. We just kind of kept our composure and just the tone of the game. At the end, you only end up with one point, but sometimes as a coach you don't always judge it on the final outcome. There's a tuckered-out bunch in there. They worked their tails off."
The Blackhawks, who have the mothers of players, coaches and staff members along for the trip, will visit the Tampa Bay Lightning on Thursday. Florida hosts the Buffalo Sabres on Friday night.