Winnipeg improved to 10-3-1 since Paul Maurice replaced the fired Claude Noel as coach.
"A vast percentage of the league is going to be pretty rested after a 2 1/2-week break," said Wheeler, who played for the United States in Sochi, but saw limited minutes as the Americans' 13th forward. "I think it's an all-out sprint.
"There's no time to be tired."
Despite some less-than-crisp play, Maurice was pleasantly surprised by how well his team played after such a long layoff.
"It was tough at times," Maurice said, "but just from the stuff I watched the last two days (around the league), it was a better game than I thought I was going to see."
Winnipeg pulled within one point of the Coyotes as both teams chase a wild-card playoff spot, although Phoenix has two games in hand. Dallas sits in the final spot with 66 points, one better than Phoenix and Vancouver, and two ahead of Winnipeg.
Pavelec made 34 saves for the Jets, with two of his toughest stops coming in overtime.
"It wasn't an easy game for both teams. It was the first game back and we didn't know what to expect a little bit," said Pavelec, who stopped Mike Ribeiro to end the shootout.
Smith stopped 27 shots for the visitors, including a pair of scoring chances in the final seconds of regulation.
"For the most part, I felt not too bad," said Smith, who was a member of Canada's gold medal-winning team in Sochi but didn't see any playing time. "But like I said, it doesn't matter how you feel, you need to come out on the better side of things."
Hanzal put away a rebound to tie the game at 2 with Jets center Jim Slater in the penalty box 6:40 into the third period.
Winnipeg took advantage of a giveaway by Coyotes defenseman Zbynek Michalek to take the lead late in the second period. With Ekman-Larsson in the penalty box, Little intercepted Michalek's pass in the low slot and beat Smith's glove hand to make it 2-1.
The teams wasted no time reminding fans of one of the differences between international hockey and the NHL game. Winnipeg's Zach Bogosian and Phoenix's Rob Klinkhammer dropped the gloves just 78 seconds into the game after Klinkhammer shoved Bogosian's defense partner Toby Enstrom into the boards.
The Coyotes opened the scoring with Ekman-Larsson's wrist shot from the high slot that went in off the post 12:17 into the first period.
It took the Jets less than three minutes to respond, as Wheeler's shot from the corner hit Coyotes defenseman Michael Stone in the leg and bounced into the net. Smith was distracted earlier in the sequence by Winnipeg forward Dustin Byfuglien, and the Coyotes argued for an interference call.
Smith and Coyotes coach Dave Tippett both said they disagreed with the non-call.
Jocelyne Larocque, a defenseman for Canada's Olympic gold medal-winning women's hockey team, performed the ceremonial puck drop. ... The Jets welcomed back Slater, who missed 52 games with a sports hernia, and left wing Evander Kane, who sat out the last six games before the Olympic break with a hand injury. ... The Jets head to Nashville for a one-game road trip Saturday, while the Coyotes play in Denver on Friday night before heading home. ... The teams have one remaining meeting, April 1 in Arizona.