Schneider scored with 1:29 left in overtime on Anaheim's 38th shot of the game, lifting the defending Stanley Cup champion Ducks to a 2-1 victory over the Avalanche on Wednesday night.
Chris Pronger tied the game early in the third period, and the Ducks, who took just 16 shots in Tuesday's 2-0 win at San Jose, had plenty other scoring chances against Budaj that just slid wide of the net.
"We played a lot of hockey in their end tonight, and I think we just wore them down," Schneider said. "I thought our forwards did a great job of getting in on the forecheck and we controlled an awful lot of the play down low. It should have been a four or five-goal game, but their goalie stood on his head all night.
"We generated a lot of chances. And if we do that consistently, we're going to win a lot of games. You can sense that some of the guys have their swagger back a little bit. That little cockiness is important to have on a winning club."
Anaheim goalie Jonas Hiller faced just 12 shots in his fifth start of the season, while Jean-Sebastien Giguere got the night off after posting his first shutout of the campaign. Colorado's shot total was just one more than the Anaheim record for fewest by an opponent.
Each team had only one power play chance -- until Colorado center Cody McCormick received a delay-of-game penalty for clearing the puck over the glass with 22.2 seconds left in regulation. The Avalanche survived that scare before Schneider scored his fifth goal of the season.
Chris Kunitz carried the puck into the zone on a 2-on-1 rush and fed a cross-ice pass to Schneider, whose wrist shot beat Budaj high to the glove side as defenseman Scott Hannan flopped on his stomach in an attempt to block it.
"I was hoping for a shootout, but Schneider made a nice shot," Budaj said. "I think I had a good angle on it. Maybe I was cheating a little bit to the right side, and maybe I was open on my glove side. I'll have to look at the video."
Hiller faced only five shots before McCormick converted Ian Laperriere's pass from behind the net at 8:33 of the second period, beating the Avalanche goalie to the stick side while Anaheim defenseman Francois Beauchemin was tying up Milan Hejduk in front of the crease.
Pronger tied it with 16:15 left in the third period. Todd Marchant carried the puck into the zone and left a drop pass for rookie Ryan Carter, whose 30-foot wrist shot was stopped by Budaj. However, he couldn't control the rebound, and Pronger backhanded the puck under the goalie's right skate for his sixth goal of the season.
"We wanted to get shots through and get second opportunities," Carter said after recording his first NHL point. "Their goaltender played really well. But we felt that if we stuck to it, eventually the puck would end up going in. I had a couple of guys in front of me, so I just tried to get the puck through. Prongs drove the net hard and made a nice play to tip it in."
Captain Joe Sakic sat out his 10th straight game with a groin injury. He missed only one over the previous three seasons combined, due to an injured jaw. Colorado left wing Ryan Smyth missed his first game of the season because of a stiff neck.
"We started a little short-handed without Smitty in the lineup," coach Joel Quenneville said. "We had to change and improvise our lines right before the game. But we worked hard and the guys battled. And Peter was outstanding tonight."
Defenseman Jordan Leopold also didn't play for the Avalanche. Leopold, who received stitches in his right leg during a practice session last week, was sent back to Denver on Tuesday after the stitches opened up in Monday's 4-2 win at Los Angeles. It was only his third game back after missing the previous 21 because of an injured wrist.
Brad May, who was traded from Colorado to Anaheim last Feb. 27, was sidelined because of a broken bone in his right foot. The injury occurred during Saturday's practice. This was the first game between the teams since that trade.
The Avalanche played back-to-back games against Anaheim and Los Angeles on the same road trip for the 11th time in franchise history -- and have never won both games. ... Budaj has allowed just six goals on 122 shots on net during Colorado's last four games. ... McCormick's goal snapped a 22-game drought. ... Anaheim has not allowed a third-period goal over its last seven home games. ... The Ducks have scored no more than two goals in any of their last five games overall. ... Colorado D Karlis Skrastins, whose NHL-record playing streak for defensemen ended at 495 games the last time these teams met on Feb. 25, 2007, has played in only 19 of Colorado's first 34 games because of a shoulder injury.