Alex Lyon made 36 saves, and Shayne Gostisbehere had two assists for the Red Wings (36-30-8), who have lost the first four of a five-game road trip (0-2-2) that concludes Monday at the Tampa Bay Lightning.
Detroit is two points behind the Philadelphia Flyers for the second wild card into the playoffs from the Eastern Conference.
“It was a gutsy, very impressive point for the guys,” Red Wings coach Derek Lalonde said. “In the circumstances, you want [two points]; [in] reality, we knew this was going to be a very tough road trip and we’re trying to get any points we can.
“We had 21 blocked shots going into the third period. A lot of will from the group. That is an effort from the group where I am proud of them.”
The Red Wings finished with 25 blocked shots and played almost the entirety of the first period without captain Dylan Larkin, who took a deflected point shot from teammate Jeff Petry off his left leg at 28 seconds. He tried to come back midway through the first but went back to the dressing room but was able to return for the start of the second period.
Detroit forced overtime when Larkin tied it 2-2 at 16:00 of the third period with a one-timer of Patrick Kane’s pass in the right circle knuckled off Bobrovsky’s shoulder.
“We played hard, blocked a lot of shots, guys were battling through the flu,” Larkin said. “We take a lot of pride off that performance, and it is something we can build off of. You saw the response when they went up 2-1 -- we battled, played for each other and stayed disciplined. It came to a shootout, and we had every opportunity to win.”