After scoring only once in six previous attempts in the tiebreaker this season, Heatley buried the winning goal in the fifth round of the shootout on Thursday night to lift the Minnesota Wild to a 3-2 victory over the Phoenix Coyotes.
"I know he is aggressive and moves around," Heatley said. "When I came in on him, I saw an opening and went to the backhand."
Hackett took over for Josh Harding, who left with an undisclosed lower body injury at 11:38 of the second period. Hackett, recalled from AHL Houston on March 1, stopped 17 of 19 shots to improve to 3-2.
"The win was impressive," Hackett said. "I let some pretty big rebounds out there, but the guys really battled. This was a great character win."
Harding, who left after stopping a drive from Ekman-Larsson, will be evaluated on Friday. He finished with 24 saves. Hackett played in his eighth game of the season.
The Wild won for the first time in six games. The Coyotes have lost five straight. Phoenix remained one point ahead of San Jose for seventh place in the Western Conference. The Sharks will visit the Coyotes on Saturday.
Phoenix has been outscored 10-1 in the first period of its last five games.
"We're not the kind of team geared to come from behind," LaBarbera said. "We play better with a lead, and that's our identity. When you're chasing the game, it makes everything much more difficult on everybody."
Kyle Brodziak and Steven Kampfer scored first-period goals for the Wild.
Raffi Torres got the Coyotes within 2-1 when he scored at 1:40 of the third period, netting his 11th goal of the season off a pass from defenseman Michael Stone. Just 1:05 later, Lauri Korpikoski tied it when he converted a pass from Antoine Vermette for his 15th goal.
"Phoenix played like a desperate team," Wild coach Mike Yeo said.
Minnesota scored two goals within 1:58 early in the opening period.
Defenseman Keith Yandle's pass through the middle was intercepted by Darroll Powe, whose 25-foot drive was tipped in by Brodziak at 4:06. Kampfer, recalled from Houston on March 3, scored his first of the season on a wrist shot from inside the left circle at 5:04.
The Coyotes outshot the Wild 32-15 through the first two periods, but couldn't score.
"We had over 80 attempts at the net, and you need to make some of these count," Phoenix coach Dave Tippett said. "You can't put yourself in holes like that. That's a recipe for disaster, and that's not the first time we've seen that."
Stone's assist on Torres' goal was his first NHL point. ... Phoenix's Martin Hanzal was struck in the face by a high stick late in the first period, and didn't return.