The defenseman buried a slap shot from the left circle with 1:46 left in the third period to send Tuesday's game against the Colorado Avalanche into overtime. Minnesota went on to win 3-2 in a shootout.
"I'm so happy for Schultzy to get that goal," Koivu said. "It's the biggest goal for us so far this season."
The goal was Schultz's first since Dec. 20 at St. Louis and just the 21st of his seven-year career.
"Pretty much every goal I score is a shock to me," Schultz said. "So when it went in I was pretty excited."
Niklas Backstrom stopped 24 shots and stymied both Milan Hejduk and Marek Svatos following Wojtek Wolski's shootout goal as Minnesota improved to 4-1-1 against Colorado this season and 8-1-2 against its Northwest Division rival in the last 11 meetings.
Ryan Smyth scored his team-leading 26th goal and Cody McLeod scored his first since Feb. 5, but Colorado dropped to 3-8-1 in its last 12 contests. Budaj finished with 26 saves but failed to earn his fourth win in his last five games thanks in part to Schultz squeezing in a difficult shot in the final minutes.
"Peter was great," Avalanche coach Tony Granato said. "They were able to find a way to take a shot from a bad angle that went off a stick and went in, so they got a break there."
Minnesota, playing at home after nine of 10 on the road, improved to 3-5-4 in its last 11 games and avenged a 2-1 shootout loss to the Avalanche in Denver last Thursday. The home points are even more important considering the Wild return to the road for five of the next six games.
"Those are the efforts you need this time of year," Schultz said. "We need everyone in this locker room. We've said it before: You can't have passengers. We've had that maybe of late where we have certain guys. Everyone in this locker room needs to step up. That's how you get goals to win games."
Minnesota was forced to come back twice in the game after first falling behind midway in the second period. Colorado got the scoring started when McLeod's centering attempt from behind the net hit Backstrom and flipped high off the ice and off Kurtis Foster's helmet before it fluttered over the Minnesota netminder. The goal was only McLeod's second point in his previous 16 games.
"I was a little discouraged after that goal," Wild coach Jacques Lemaire said. "We got no breaks, but we worked hard enough to get back in the game."
Stephane Veilleux's goal tied the score 1:44 later, but Smyth scored for the second straight game to pull the Avalanche back in front.
Smyth tipped Wolski's shot with his back turned to the net, beating Backstrom between the pads.
Injury-riddled Colorado killed a pair of ensuing penalties and stayed in front despite playing a pair of defensemen making their NHL debuts. But Schultz's shot found an opening above Budaj's right shoulder to set up overtime.
The Wild improved to 5-3 in shootouts and 4-1-1 against the Avalanche this season. Colorado dropped to 9-2 in shootouts.
Avalanche defenseman Daniel Tjarnqvist was scratched with a gash above his eye suffered on Sunday in Vancouver. ... Fellow defenseman Adam Foote missed his third game due to a head injury, prompting Colorado to call up Lake Erie defenseman Derek Peltier, a native of Plymouth, Minn., and a University of Minnesota alum. Peltier and defenseman Mike Vernace, who was called up from Lake Erie on Monday, both made their NHL debuts Tuesday. ... Right winger Darcy Tucker was scratched as a precaution after his back tightened up during the team's morning skate. He had scored goals in each of the Avalanche's previous two contests. ... Foster made his home debut and played for just the second time this season following an extended rehab from a broken leg suffered March 19, 2008, at San Jose. Foster played at Los Angeles on March 7 but was scratched in the Wild's ensuing five games.