Korpikoski gave Phoenix the lead for good with his second goal of the game, and Taylor Pyatt and David Schlemko also scored in the Coyotes' 5-2 victory against the Anaheim Ducks at the Honda Center.
Coyotes captain Shane Doan added an empty-net goal with 42 seconds remaining and had two assists. Ilya Bryzgalov made 36 saves against his former club to help the Coyotes earn a split of the six-game season series and move into fifth place in the Western Conference.
"You're going to drive yourself crazy if you look at those standings that hard every day," Coyotes coach Dave Tippett said. "We have the focus right now that every game is going to be the game that puts you in the playoffs, and we have to play every one just like it's a playoff game."
Corey Perry scored both Anaheim goals, and Dan Ellis stopped 17 of 21 shots through two periods before he was replaced by Ray Emery. The 10th-place Ducks are two points and two positions behind eight-place Calgary and the postseason cutoff in the West. Anaheim will host St. Louis on Wednesday.
"We didn't have a very good start to the hockey game," Ducks coach Randy Carlyle said. "That was the biggest issue I have as a coach. We didn't come out of the gate firing like we normally do. We have had great starts here before. Tonight, it just seemed like we were a half of a step behind. We got our game going in the second period and we did a lot of good things."
Emery, who stopped all 10 shots he faced in his Anaheim debut, got into an NHL game for the first time since Feb. 1, 2010, when he was with Philadelphia. A month later, Emery underwent hip surgery.
He was signed by the Ducks last month after All-Star goalie Jonas Hiller went on the injured list because of vertigo. Emery has been serving as the backup to Ellis, obtained from Tampa Bay on Feb. 24.
"I've been waiting to get in the net," Emery said. "I didn't want it to be under that circumstance. I tried to give the boys a chance to stick around in the game."
Perry tied it 2-all at 15:46 of the second period with his 36th goal, redirecting a slap shot by rookie Cam Fowler over Bryzgalov's right shoulder on a power play created by a penalty for too many men on the ice.
Phoenix regained the lead 61 seconds later.
Ducks forward Todd Marchant tried to sweep the puck out of his zone while backpedaling in the right circle and fanned. Korpikoski swooped around the flat-footed Marchant, swerved past defenseman Lubomir Visnovsky, and slid his 17th goal between Ellis' pads.
Marchant was sent off 27 seconds later for high-sticking Korpikoski, and Schlemko made it 4-2 three seconds after the penalty expired.
Doan broke his stick on a slap shot during a power play, and ended up with an interference penalty at 15:05 of the first. Just 28 seconds after leaving the penalty box, Doan set up Korpikoski's first goal for a 2-1 Coyotes lead.
"The fun thing about being on this team is that we count on every single guy," Doan said. "Korpikoski was incredible. You've got to give him credit for creating something out of nothing twice."
Anaheim defenseman Toni Lydman discarded a broken stick in the Phoenix zone and was trying to guard Korpikoski in the left circle of the offensive end when Korpikoski scored with a wrist shot.
"You have to tip your hat to Bryz," said Marchant, a teammate of Bryzgalov's for parts of three seasons. "He really kept them in there and made some big stops. It could have been a much different game if we had gotten some by him early."
Material from wire services and team media was used in this report.