"It was disappointing to lose after having a 2-0 lead," Coyotes captain Shane Doan said. "You expect to win at that point, and unfortunately we didn't. We had opportunities on the power play and we didn't capitalize on them. We have to be better than that."
Mike Smith was excellent in making with 41 saves, but he couldn't stop Eberle and Gagner in the shootout.
"Those were two of the best penalty shots that I have seen in my life," Krueger said. "Smith is one of the best goalies in the league, those goals were just world class."
The Coyotes started the scoring after some prolonged pressure when Chipchura shoveled a shot toward the net that just trickled across the goal line before Oilers starter Nikolai Khabibulin could reach back to glove it.
Edmonton had a couple of opportunities to tie the game up late in the first, both short-handed. Eric Belanger and then Gagner were able to break loose on breakaways, but both were stoned by Smith.
The Oilers came close again five minutes into the second frame as Ryan Jones lifted a rebound over Smith, only to see defenseman Keith Yandle swoop in and glove it out of harm's way.
Phoenix made it 2-0 midway through the second with Nick Schultz serving a double minor for high-sticking. Edmonton had killed off the bulk of the penalty before a Boedker shot got past Khabibulin and hit the post, allowing Lombardi to sweep in the rebound.
Edmonton finally got on the board with 3:38 remaining in the second as Nail Yakupov showed some speed hustling for a dump in and send a backhand pass to Eberle who chipped it past Smith.
The Oilers tied the game eight minutes into the third on the power play as Ryan Smyth tipped Justin Schultz's shot and it went straight to Hartikainen at the side of the net for his first of the season.
Edmonton had the best chance in overtime with a power play, but Smith was able to make a dramatic glove save on a hard shot by Gagner.
Khabibulin stopped Boedker and David Rundblad in the shootout and finished with 34 saves.
The Oilers now embark on their extended trip, starting Monday in Chicago, with the Canadian men's curling championships occupying Rexall Place for the next two weeks.
The opening game of the trip might be the toughest as the Oilers will face the Blackhawks, who haven't lost in regulation yet this season.
"We weren't the greatest team at home during this run," Eberle said. "At least with this win we have some momentum going into the road trip."
Edmonton forward Taylor Hall served the first of a two-game suspension for his hit on Minnesota's Cal Clutterbuck on Thursday. ... Jones played his first game of the season since sustaining an eye injury during a practice session during the lockout. ... Edmonton D Ryan Whitney was a healthy scratch for the fifth time this season. ... Phoenix was without F Radim Vrbata (lower body) and D Derek Morris (upper body).
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EDMONTON, CANADA - FEBRUARY 23 : Ryan Jones #28 of the Edmonton Oilers makes his return to the line up in a game...