Columbus coach Ken Hitchcock successfully changed his shootout lineup and goaltender Fredrik Norrena stopped all three Dallas attempts to send the Blue Jackets to a 3-2 victory over the Stars on Friday night.
Chimera beat Stars goaltender Marty Turco for the only conversion by either team.
The Stars had been 6-3 in shootouts this season and 18-4 overall in the tiebreaker.
"We were joking that we better not get into a shootout," Chimera said. "But that was exciting. That's a fun time of the game."
Columbus was 2-5 for the season in the shootout prior to Friday, and Hitchcock decided at a recent practice to alter his lineup.
"What do you have to lose?" Hitchcock said. "We haven't done well in shootouts. You have to change it up from time to time."
Jokinen had been successful on 15 of his 22 career shootout attempts prior to Friday night, but Norrena stood his ground and forced Jokinen to steer the puck wide on the backhand.
"It was pretty close," Norrena said. "I don't know if I touched his stick or he just missed it. I know he's really good at that move."
When Jokinen missed, failing to send the shootout into a fourth round, the Blue Jackets went onto the ice to celebrate.
"We seem to play well against the better teams and Dallas is one of those teams," Chimera said. "It was nice to have a game like this. Our whole team played well."
Modano scored his 497th career goal and Darryl Sydor had a goal and an assist for Dallas, which had been 12-3-3 in its previous 18 games including an 8-1-1 run at home. The Stars were playing in their fourth straight overtime game to match a club record.
Modano's second-period goal, his first in eight games and 12th of the season to pull the Stars even after falling into a 2-0 deficit, leaves him five behind Joe Mullen for the career record among U.S.-born players.
Modano got his second goal in 13 games since missing 23 straight games because of a hip injury that has lingered.
"It's still there, still nagging me so I think it's something I just have to deal with," Modano said. "Some days are good and some days are bad."
The Stars were on the second leg of back-to-back games and were playing their third game in four nights. Dallas lost on the road in overtime to the Florida Panthers on Thursday night, 2-1.
"It took a while for us to get going," Stars coach Dave Tippett said. "I think we were still on the plane in the first period."
Hitchcock won in Dallas behind the Columbus bench for the second time in as many trips this season. Columbus beat Dallas 3-1 on Dec. 12.
Malhotra, who played for the Stars from 2002-03, scored on a one-timer from the slot off a pass from Chimera at 11:34 of the first period to put the Blue Jackets in front. Turco had fallen and was out of position on Malhotra's seventh goal of the season.
Columbus took a 2-0 lead at 5:21 of the second period when Fedorov pounced on a rebound for his 17th goal of the season.
Sydor pulled Dallas within 2-1 at 8:03 of the second period with a power-play shot from the right point for his fifth goal of the season.
Modano tied it at 2 about a minute and a half after Sydor's goal when Modano converted Jokinen's centering pass.
Mattias Norstrom was among Dallas' scratches. Norstrom has yet to make his Stars debut after being acquired on Tuesday in a trade with the Los Angeles Kings. ... Nolan Baumgartner played in his first game for Dallas after being claimed on waivers from the Philadelphia Flyers on Saturday. ... Alexander Svitov was scratched for Columbus because of an upper-body injury. ... Adam Foote of the Blue Jackets left the ice 1:34 after the opening faceoff with a sprained ankle and did not return. Foote had been checked into the boards by Modano and was helped from the ice. He won't play in Saturday night's game at Phoenix... Stars defenseman Stephane Robidas set a career high with his 16th assist.