The Ducks must await the outcome of other Western Conference series to find their next opponent. Anaheim's Corey Perry scored his first career playoff goal with 9:31 remaining, and Travis Moen added an empty-net goal with 57 seconds left.
Jean-Sebastien Giguere, getting his first start in eight games, made 26 saves for Anaheim.
Chris Pronger scored just 1:02 into the game, and Marian Gaborik tied it briefly with a short-handed goal at 15:42 of the second period. But Getzlaf scored less than a minute later.
The Ducks got off 38 shots at Minnesota goalie Niklas Backstrom.
The teams had a brief pushing match during warmups, with no officials on the ice. The Wild's Derek Boogaard and the Ducks' George Paros, their team's enforcers, exchanged words, then players from both sides crowded to centre ice. There was some yelling and pushing, but no punches thrown. The players eventually backed off.
Shortly later, Anaheim's Teemu Selanne was struck in the head by a puck and fell to the ice. He had the cut closed with about a half-dozen stitches and started the game. It wasn't immediately known who shot the puck.
Animosity between the teams had flared late in the Wild's 4-1 win at Minnesota on Tuesday night. Anaheim's Brad May received a three-game suspension on Wednesday for punching Kim Johnsson late in that contest. Johnsson, who sustained a head injury, was undergoing tests and didn't make the trip to Anaheim.
Giguere, sharp despite being out for the final three games of the regular season and all the playoffs - except the closing minutes of Game 4 - had been given time off to be with his wife and their son, who was born April 4, with an eye problem.
Ilya Bryzgalov started in Giguere's place and held the Wild to a total of four goals in the opening three games before giving up all the goals in the loss at Minnesota. Giguere replaced him late in that game.
When the fifth game began, the Ducks quickly put the Wild back on their heels, just missing on two scoring chances in the opening minute, then going up 1-0 on Pronger's slap shot from the left point.
With Boogaard off after drawing a double-minor penalty for high-sticking in the second period, Gaborik skated down the left side, took a pass from Wes Walz on the 2-on-1 break and beat Giguere on the stick side for his third of the series.
The tie lasted only 47 seconds.
Getzlaf, skating to the top of the crease, hit the left post with his wrist shot, and the puck caromed into the other side of the net for his second goal of the series.
Pronger scored when Samuel Pahlsson flicked the puck back to him on a faceoff. Pronger's low liner sailed past Backstrom on the glove side.
Notes: The Wild went 0-for-5 on power plays, including a two-man advantage for a two-minute span midway through the second period, and finished the series 2-of-27 on power plays. ... Backstrom got an assist on Gaborik's goal. ... Giguere had a club-record 36 victories during the regular season, bettering his own mark of 34 in 2002-2003. In the post-season that year, he shut out Minnesota three times as Anaheim swept the Western Conference finals. .. The Ducks won each of the opening three games of the series by one goal.