Parise and Jason Pominville scored in the shootout, lifting Minnesota to a 2-1 victory over the Toronto Maple Leafs on Wednesday night.
Parise tied the game late in the third period for Minnesota, which has won five of six and is 8-1-2 in its last 11. The Wild have been involved in three straight shootouts - winning two.
In the shootout, Parise beat Jonathan Bernier low on the left side before Josh Harding stopped Raymond. Mikko Koivu was stopped by Bernier and Phil Kessel lost control of the puck before Pominville beat Bernier through the pads for the win.
''We had little bit more of a feeling that this game was there for us if we could keep going,'' Minnesota coach Mike Yeo said.
Parise tied it with 4:17 to play in regulation when, after a turnover by Kessel, Charlie Coyle's shot from low on the right side deflected off Parise's skate and into the net.
''He made initial contact with the shoulder and the kid had his head down, he didn't have his arms up, he ran into the player, Granlund snapped his head back and obviously, the referee saw it differently, and obviously, with a five-minute match penalty, it'll be reviewed,'' said Toronto coach Randy Carlyle.
However, Minnesota heard plenty of boos from the crowd as it got off just one shot during the man-advantage.
''Even the guys that were power-play guys were coming back saying, `C'mon, we still got lots of time,' talking, saying the right things and these are the leaders of your team,'' Yeo said. ''I've been part of many games where you have something like that and frustration creeps in and it's real easy to have some type of letdown or start to deviate or get away from staying with it, trusting it, and they didn't.''
The hit on Granlund was Kadri's second action for which he will likely be hearing from the league. Kadri was not made available to the media.
Minnesota's starting goaltender, Niklas Backstrom, was run over by Kadri 7 minutes into the game, and lay flat on the ice for about 30 seconds before slowly sitting up. Kadri's elbow appeared to hit Backstrom in the head. Yeo said Backstrom has an upper-body injury.
Backstrom, starting for the first time since Oct. 28, stayed in the game until a stoppage with 10:31 left in the period before skating to the bench and heading to the dressing room. He had three saves.
''That'll be interesting to see what happens there because it looks like he got him right in the head,'' Parise said. ''That's what we're trying to get rid of. It'll be interesting to see what they decide.''
Mason Raymond scored a power-play goal for Toronto, which has scored just three regulation goals in its last four outings. Jonathan Bernier had 33 saves.
Toronto nearly won it late in overtime, but Harding got a right pad on a tip by Morgan Rielly and then reached back to grab the puck just outside the goal line.
''They're a good team in their building and at least we came up with one point. We've just got to move on,'' Bernier said.
Harding had 19 saves in relief of Backstrom. He started the past five games and was to be given the night off due to sickness. Instead, he increased his save percentage to .947, second-best on the NHL, while lowering his league-best goals-against average to 1.21.
There wasn't much he could do as Raymond gave the Maple Leafs a 1-0 lead at 7:32 of the second period, when he gathered a loose puck that hit traffic in front and tucked it behind a sprawled Harding. It was just Toronto's second power-play goal in 16 chances over six games.
Minnesota had two power plays early in the third period, but came no closer than Koivu hitting the crossbar.
NOTES: Wild D Ryan Suter has averaged 36:06 of ice time in the last three games. ... Toronto RW Colton Orr returned after missing two games with an undisclosed injury. ... Clayton Stoner was back on the Minnesota blue line after missing Saturday's game with a leg injury. ... Kessel, who played for the University of Minnesota in 2005-06, played his 300th game with the Maple Leafs. He has 129 goals and 143 assists in those contests. ... The Wild played its 500th game at Xcel Energy Center, including regular season and playoffs. ... This was just Toronto's fifth game at the arena, fewest all-time among Minnesota opponents.