ANAHEIM, Calif. (AP) -- Every time it appears the Anaheim Mighty Ducks are ready to sink, someone steps up to rescue them.

This time, it was Oleg Tverdovsky. The veteran defenseman, in his second stint with the Ducks, scored with 1:13 left in overtime Sunday night as Anaheim rallied from two goals down to keep their flickering playoff hopes alive with a 4-3 victory over the Phoenix Coyotes.

Teemu Selanne scored twice and Fredrik Olausson got the tying goal on a power play early in the third period, helping the Ducks climb within two points of Phoenix, San Jose and Edmonton for the eighth and final Western Conference playoff berth.

"Today was do-or-die for us," said center Matt Cullen, who set up the winning goal. "We got down early, but just did not give up. When your whole season is on the line, you're able to put things into perspective."

Phoenix goalie Sean Burke, who made 37 saves, stopped all four shots during an overtime power play after Lyle Odelein was sent off for holding Matt Cullen at 1:44.

But the Ducks, who have outshot their opponents 16-1 in their last three overtime periods, finally scored on their fifth shot of the extra period.

Tverdovsky, who returned to the Ducks this season in a draft-day trade with the Coyotes, used Benoit Hogue as a screen and one-timed a pass from Cullen to beat Burke for his 15th goal and 29th point in 30 games. He has scored two of Anaheim's three overtime goals this season.

"We wanted to win this game, and we need as many points as we can get," said Tverdovsky, a number one draft pick by the Ducks who was dealt away for Selanne. "We still have a lot of work to do these next two weeks. We came out sleeping tonight, and we can't do that. It's a good thing we woke up,"

Hogue, Greg Adams and rookie Trevor Letowski scored in the first period for Phoenix. The Coyotes played without captain Keith Tkachuk, who finished the two-game suspension he received for high-sticking Colorado defenseman Aaron Miller on March 23.

The defeat extended Phoenix's losing streak to seven games -- the longest since the franchise moved from Winnipeg in 1996. The Coyotes are 1-22-3 when leading scorer Jeremy Roenick has not recorded a point.

"We're not finding our legs right now," Burke said. "We're on the ropes and we're not fighting back. We're absolutely horrible. There's not one guy in this room that's playing well right now. We're the one team fighting for a playoff position that shouldn't even be in this position."

Anaheim goalie Guy Hebert -- yanked after surrendering five goals on 24 shots in the first two periods of Friday night's loss at Vancouver -- was beaten on three of the Coyotes' first 13 shots.

The next one -- a bullet by Hogue with 1:06 left in the opening period -- struck Hebert flush on the mask and left him dazed for several moments. But he stayed in the game and stopped the Coyotes' final 11 shots to finish with 21 saves.

Selanne narrowed the gap to 3-2 at 3:48 of the second with his 30th goal and second of the game. It was the sixth time Selanne reached the 30-goal mark in his eight NHL seasons.

The Ducks, 9-for-34 on the power play in seven games, tied it after Teppo Numminen was sent off for holding Selanne in front of the Phoenix net 13 seconds into the third. Paul Kariya threaded a cross-ice pass under Odelein's stick, and Olausson beat Burke between the pads from the right of the crease.

"We're disappointed that we didn't get the two points, but we've got to be happy that we got a point out of it," coach Bob Francis said. "They came at us hard and in waves. That's what we wanted to do to them, but it's tough to attack when you're chasing the puck in your own zone."

Selanne was deprived of the game-winner -- and his 17th career hat trick -- with 25 seconds left in regulation. Burke slid across the crease to rob him after Kariya set up Selanne with a perfect pass from behind the net.