ANAHEIM, Calif. (AP) -- Losing four in a row was bad enough for the Anaheim Mighty Ducks. A third straight loss in overtime would've been really hard to take. Petr Sykora helped the Ducks avoid that fate when he scored 3:43 into overtime of Anaheim's 2-1 victory Sunday over the Phoenix Coyotes. Jean-Sebastien Giguere made 27 saves and Steve Rucchin scored a short-handed goal for the Mighty Ducks, who returned from a six-game road trip that ended with overtime losses at St. Louis and Phoenix. "They were really desperate," Phoenix goalie Sean Burke said. "We knew they wanted to come back from last night, and they played like it. They were really flying." Giguere, last season's playoff MVP, improved to 2-8. His other victory also came in overtime, Oct. 22 against Philadelphia, when he allowed the tying goal in the final second or regulation. "Hopefully tonight helps with my confidence. I'll go home feeling good," Giguere said. "We played for 60 minutes and the defensive-zone coverage was much better." Sykora ended it with a wrist shot from the middle of the left circle that beat Burke high to the glove side. It was his second career regular-season overtime goal to go along with the two he scored in last season's playoffs when Anaheim advanced to the Stanley Cup finals. "We let them play too much in our own end, especially in the third period. It took a perfect shot by Sykora to beat us," Phoenix coach Bob Francis said. Sykora's fourth goal of the season was the only shot that got past Burke, who faced 29 shots after replacing Zac Bierk at the start of the second period. Bierk, making his fourth start, stopped 16 shots before leaving because of a hip flexor. Sergei Fedorov assisted on the game-winner for his first point in five games and the 965th of his career, tying Maurice Richard for 71st place on the NHL career list. Ladislav Nagy, who had two goals against the Ducks in Saturday's win at Phoenix, tied it at 18:34 of the second after Giguere stopped Phoenix's first 19 shots. Nagy's eighth goal in 13 games came on a turnaround wrist shot from the top of the right circle that beat a screened Giguere. Rucchin, who had two goals Saturday, opened the scoring 14:17 in with Anaheim's first short-handed goal of the season. The Ducks captain poked the puck off David Tanabe's stick at the Phoenix blue line, then took it away at the right boards. He cut toward the net and slipped his sixth goal under Bierk's stick. It was Rucchin's sixth career short-handed goal and first since last December at Chicago. "We can't give up 45 shots and expect to win in this league," Phoenix captain Shane Doan said. "We gave up a lot of scoring chances in our own zone and played kind of sloppy, but our goalie kept us in it."