Saku Koivu had the other goal for Anaheim, which opened the season with two road wins and will enjoy a rare three-day rest in this year's compressed schedule before hosting Vancouver in its home opener Friday.
Signed as a free agent last summer, Winnik has found instant chemistry on a line with Koivu and Andrew Cogliano. All three were in on Winnik's go-ahead goal at 4:02 of the third period, which broke a 3-3 tie.
Curtis Glencross had two goals, and Lee Stempniak and Alex Tanguay also scored for Calgary, which opened with consecutive home losses.
The culprit on the go-ahead goal was Tanguay, who was 150 feet from where it was scored. His pass into the slot on a Flames rush was picked off by Cogliano, who promptly turned and led a rush up ice that was eventually finished off by Winnik.
Winnik, with his third and fourth goals of the season, is tied with Chicago's Marian Hossa for the most goals in the very young NHL season and is suddenly just seven goals off his career high.
Getzlaf added his second goal of the night at 11:15 to make it 5-3, and, although the Flames got back to within one on Stempniak's breakaway goal three minutes later, Calgary was unable to get the tying goal past Jonas Hiller.
On the heels of a 4-1 loss Sunday night to the San Jose Sharks in which Calgary led 1-0 after one period, only to fall apart, the Flames got off to the worst possible start. Fans were still making their way to the seats when Anaheim opened the scoring at 1:06 on a nifty deflection by Getzlaf of Toni Lydman's point shot.
Koivu flicked in Cogliano's centering pass at 7:23 to make it 2-0, and Winnik's shot deflected off Wideman and behind Miikka Kiprusoff 3 minutes later.
With Anaheim up 3-0 on the scoreboard, 9-2 on the shot clock, and having sucked all the energy out of the Scotiabank Saddledome's normally boisterous sea of red fans, the Flames were looking for a spark
-- and they got one when Lydman was sent off for cross-checking at 16:15.
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With new addition Dennis Wideman quarterbacking the power play, it took Calgary 39 seconds to connect when Wideman's shot was deflected in by Glencross.
Calgary cut the deficit to 3-2 with 26 seconds left in the first after Tanguay beat Hiller over the blocker on a wrist shot.
A penalty with one second left in the first put the Flames back onto the power play to open up the second period and again it was Glencross connecting with another deflection to tie it 3-3.
Calgary outshot the Ducks 14-3 in the second and could have taken the lead if not for some sharp saves from Hiller, his best being a pad stop of Stempniak on a breakaway that would have put Calgary in front.
Hiller finished the game with 21 saves, while Kiprusoff stopped 19 shots.
NOTES: The appointment for Flames C Roman Cervenka (blood clots) to see a specialist in Phoenix about his condition was postponed until Tuesday. ... Seven of Winnik's 40 career goals have come against the Flames. His career high for goals in a season is 11. ... Calgary made two lineup changes, inserting center Blair Jones and defenseman T.J. Brodie in place of left wing Steve Begin and defenseman Derek Smith. Jones played in his 100th NHL game. ... Anaheim welcomed back defenseman Cam Fowler after he missed Saturday's opener with the flu. ... The Flames have eight more sets of back-to-back games. ... Anaheim right wing Teemu Selanne is tied with Phil Esposito for third all-time with 249 career power-play goals.
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