After Jokinen's goal, Marc-Andre Fleury made a pad save on Gabriel Landeskog's shot, snapping Colorado's six-game winning streak and denying Varlamov franchise records for most home and overall wins in a season.
Colorado coach Patrick Roy said his team might have taken the Penguins lightly after seeing Sydney Crosby and Chris Kunitz joining center Evgeni Malkin (foot) in street clothes, leaving Pittsburgh without its top three scorers.
''Tonight when we saw Crosby not in the lineup, Kunitz not in the lineup, on and on, I think it was a normal reaction to say, 'Hey, we have an easier game tonight,''' Roy said.
Locked into the No. 2 seed in the Eastern Conference, the Penguins sat several of their regulars. Crosby missed his first game of the season because of an unspecified injury. He has never played all 82 games in a season. They also were without defensemen Brooks Orpik and Olli Maatta, scratched with unspecified injuries, just like Kunitz.
''I probably would have done the same,'' Roy said. ''We're thinking of doing the same at the end depending where we are in the standings. We're going to rest Varly probably the last two games. Absolutely not (offended). I think they did what was the right thing for their team. The only sad part there's a lot of people coming here to see Sidney Crosby play. That's fine, that's part of our business.''
Landeskog had mixed feelings about Crosby sitting this one out.
''Of course he's the best player in the league,'' Landeskog said. ''I would have liked playing against him. But at the same time he took a slap shot off my knee the last time we played against him.''
The Penguins played with precision and poise despite having nothing on the line and a bevy of backups.
''Yeah we did,'' Brandon Sutter after posting his first multiple-goal game of the season. ''We didn't have a great game last night (a 4-0 loss at Minnesota) but to come back here 24 hours later and play the way we did was great, especially with the lineup we had. Everyone played well, top to bottom. You give guys an opportunity it's amazing what can happen. A lot of guys played great, especially our goaltender. He was awesome.''
Fleury, who stopped all three shots in the shootout, had 39 saves, including one in the closing seconds of overtime after Penguins defenseman Paul Martin was sent to the penalty box with 38 seconds remaining for delay of game after he knocked the puck over the glass in the defensive zone.
''It's a credit tto our team to be able to battle without a lot of key guys,'' Fleury said.
The Avs lost for just the fifth time in 39 one-goal games this season (28-5-6), and they can blame their 0-for-5 performance on power plays, something Fleury had a lot to do with.
After falling behind 2-0 on Sutter's pair of second-period goals, Colorado scored twice in the third period. Ryan O'Reilly scored his team-leading 28th goal of the season 18 seconds into the period, and Patrick Bordeleau redirected defenseman Tyson Barrie's shot into the net with 3:13 left.
Varlamov stopped all 31 shots on Saturday in St. Louis to earn his 40th win of the season, tying Roy's franchise record. He finished 24-10-3 on home ice, matching Roy's record for home wins set in 2000-01, when the Avs won the Stanley Cup for a second time.
With the point they picked up, the Avs are two ahead of Chicago for second place in the Central Division, which would give them home-ice advantage in their first-round playoff matchup.
''To get two points would have made us feel better, but at least we got one,'' Bordeleau said.
NOTES: The Penguins avenged a 1-0 loss to Colorado at home on Oct. 21. ... Avalanche D Cory Sarich missed his third straight game with a back injury.
Follow AP Sports Writer Arnie Melendrez Stapleton on Twitter: https://twitter.com/arniestapleton