Shane Doan scored his second goal of the game during a power play 1:37 into overtime to lift the Coyotes to a 5-4 victory over the Oilers.
Edmonton scored two goals 49 seconds apart before the midpoint of the third, tying it 4-4 and forcing overtime.
Doan then finished off Phoenix's win.
"One of their [defensemen] lost his stick up high and that made it a 4-on-2 and really let me creep in," Doan said. "I was just trying to hit the net and it found a hole."
Doan's winner was scored after Fernando Pisani was called for tripping.
"It's one of those nights that we probably should have had a better result," Oilers coach Pat Quinn said. "We had four bizarre goals against us. That one in overtime was a tough one. The back referee calls it from 100 feet away in a battle for the puck."
Oilers assistant captain Sheldon Souray said his team will take comfort in rallying to force overtime.
"We'll take the positives out of it, we came back, we got a point," he said. "It's a good way to get a little momentum, even though we lost the game we'll take a little of the momentum we gained in the third period and roll with it."
The Coyotes scored 12 minutes in as a flubbed faceoff outside of the Edmonton blue line led to Vrbata's breakaway. He tucked the puck between the pads of Oilers starter Jeff Deslauriers.
The Coyotes went up 2-0 seven minutes into the second period as Deslauriers allowed a big rebound on Vernon Fiddler's shot. Doan got to it and backhanded his 11th goal into a wide-open net.
Edmonton got within a goal 4 minutes later on the power play, as Brule crept in from the sideboards and fired a shot past goalie Ilya Bryzgalov.
But Phoenix regained the lead 1:02 later. Deslauriers casually allowed a dump-in to come out to Hanzal without an Oilers defender in sight. Hanzal whacked the puck in to make it 3-2.
The Coyotes restored their two-goal advantage with just over two minutes left on another Edmonton mistake. Robert Nilsson gave up the puck in his zone to Vrbata, who fed it across for a quick shot from Prucha that made it 4-2 after 40 minutes.
Edmonton had 18 shots in the second period to Phoenix's nine.
Phoenix appeared to take a 5-2 lead 6 minutes into the third, but Aucoin's goal was waved off due to goaltender interference.
"The ref made that call immediately, it's not like he questioned the call," Doan said. "He said [Ed Jovanovski] had backed in the crease or something. It was a tough one to swallow. At least it ended up working out in the end for us."
Phoenix coach Dave Tippett was surprised the goal was disallowed.
"They told me that Jovo was in the crease, but from what I saw, that wasn't the case, so I'll leave it at that," he said. "It is frustrating, but our guys hung in there. We made our point with the referees, thought it was not a very good call, made our point and let it be, then got back to playing hockey."
The Oilers rebounded to tie it with goals 49 seconds apart.
Sam Gagner stole a puck from behind the Phoenix net and fed it to a pinching Grebeshkov to make it 4-3. The Oilers got even less than a minute later as Shawn Horcoff's shot rebounded into the air and was pushed home by Penner for his 20th of the season.
The Oilers (16-22-5) had planned to take a golfing trip to Palm Springs during a four-day break this weekend, but canceled it because of their poor position in the standings. They will hold a minicamp instead. ... Pisani had been out since Nov. 15 because of his ulcerative colitis condition. ... The Oilers were without second-leading scorer D Lubomir Visnovsky (ankle). ... Quinn said G Nikolai Khabibulin, out since Nov. 21, is nearing an eight-week evaluation window and might need season-ending back surgery if progress doesn't happen soon. ... Oilers D Steve Staios was helped off the ice after blocking a shot late in the third. ... The Coyotes were without leading goal-scorer Scottie Upshall (upper body). ... Phoenix D Jim Vandermeer, who had missed four games, returned.