Bobrovsky, who relieved Steve Mason 31 seconds into the second period, stopped all 21 shots he faced through regulation and overtime before denying Sam Gagner and Ales Hemsky in the shootout as the Columbus Blue Jackets earned a 4-3 victory at Nationwide Arena.
Derek McKenzie, Vinny Prospal and Jack Johnson scored in regulation for Columbus (7-12-4), which has now won back-to-back games. Artem Anisimov scored in the first round of the shootout before Mark Letestu sealed the deal when he beat Oilers goalie Devan Dubnyk in the third round.
"I sense guys [have] a little more confidence," Columbus coach Todd Richards said. "It's nice to see guys get rewarded for their hard work and effort."
Jeff Petry, Ryan Whitney and Magnus Paajarvi scored for the Oilers (8-10-4), who have lost three in a row. They are now 1-2-2 on their nine-game road trip, which continues Thursday night at Detroit. They've been outshot 111-67 on the trip thus far.
"Bobrovsky has to be the difference maker here for the point that we lost," Oilers coach Ralph Krueger said.
Edmonton needed just 4:23 to get on the scoreboard as Petry tallied his third goal of the season to give the Oilers a 1-0 lead. With the teams at even strength, Petry took a pass from Eric Belanger and let go a wrister from the point that found its way through a crowd and past Mason. It was Petry's fifth point in as many games after he was held pointless through his first 17 appearances this season.
MacKenzie tied things up for Columbus just 3:31 later when he took a nice feed from Jared Boll and ripped a wrister from the right circle past Dubnyk. It was MacKenzie's third goal of the season and snapped a seven-game scoring drought.
Prospal gave the Blue Jackets their first lead of the night with 6:15 remaining in the opening period. With Columbus on a power play, Letestu let go a soft wrist shot from the point that was denied by Dubnyk. But Prospal parked himself in front of the net and managed to jam the rebound over the goal line to make it 2-1. It was Prospal's 10th point in the past 13 games.
The lead didn't last long, however, as Whitney made it a 2-2 game with 1:17 left in the first. Whitney, who also scored last Friday at St. Louis, took a pretty feed from Ryan Nugent-Hopkins and fired a wrister from the top of the right circle that beat Mason to the far side. Taylor Hall also picked up an assist, his team-leading 15th of the season.
"I think we had some stretches where we played well," Whitney said. "We've got to start putting points together. Us not getting two [points] is frustrating."
Paajarvi regained the lead for Edmonton just 31 seconds into the second period. Paajarvi, who ended a four-game drought Sunday night at Minnesota, seized control of the puck in the slot after it trickled away from Gagner and quickly snapped it past Mason to make it 3-2. The goal prompted Richards to pull Mason, who was beaten three times on seven shots.
"You really never know how they're going to respond to it," Richards said. "He came in, in relief, and did a great job."
Columbus defenseman Jack Johnson tied the game for the third time midway through the second period. Johnson, who had just one goal in his first 18 games, one-timed a feed from Derick Brassard in the slot past Dubnyk to make it 3-3.
"Six goals in the first two periods – that's quite a bit, especially for us," Prospal said. "We have been playing in a lot of tight games lately. We were behind and we had to go and create some offense. Sergei stepped in and he really shut the door. That was probably the biggest difference in the game for us – him making those saves."
Edmonton had the best scoring chance in overtime. After Nick Foligno was whistled for closing his hand on the puck, Nugent-Hopkins fed Jordan Eberle at the left side of the net for what appeared to be a sure goal. But Bobrovsky managed to make a sprawling pad save to preserve the 3-3 tie.
"I just tried to calm the puck down," Eberle said. "It was rolling and he made a great save."
Material from team media was used in this report