"We're not happy about that," said Matt Duchene, who had two assists. "I don't think there was really a big breakdown on that sequence, but we've just got to find a way to get it for him."
Colorado won for the seventh time in nine games to maintain its hold on second place in the Central Division ahead of the Chicago Blackhawks.
"Our goalie was without a doubt the first star of the game, but I thought our guys did a better job in the third period," Avalanche coach Patrick Roy said. "I mean, we played more sound hockey and made better decisions in our blue line and neutral zone, but it's a big win for us."
Lehner made 19 saves in his second straight start for Ottawa, which is on a 2-5-2 skid that has put a serious dent in its Stanley Cup Playoff hopes.
The Senators blew a three-goal lead with 3:22 remaining in regulation in a 5-4 overtime loss against the Montreal Canadiens on Saturday at Bell Centre.
"We really wanted to rebound from last game and just go out and work hard, just try to work and say within our structure," Lehner said. "We did, and I thought we played well today, and again, a little bit of the same story line as the whole season: a few mistakes, and their goalie played great."
Ottawa (28-26-13) is 12th in the Eastern Conference with 69 points, seven behind the eighth playoff spot.
"No matter what happens, you know, we're going to push to the end," said defenseman Chris Phillips, who has made the playoffs in 13 of his 15 seasons with the Senators. "And that's what we've been talking about, game to game, is going and trying to play the game as hard as we can, mistake free, and let the results take care of themselves, and they haven't gone our way the last couple but that can't change the way that we approach the games."
Senators No. 1 goalie Craig Anderson remains sidelined by an upper-body injury that caused him to leave in the third period of Ottawa's 4-3 overtime loss to the Nashville Predators on Monday.
"I'm going to go day to day and see how he is," Senators coach Paul MacLean said.
Avalanche center Paul Stastny missed his fourth game in a row because of a back injury.
Varlamov made a big glove save on Senators rookie defenseman Cody Ceci at 7:12 of the second on a shot from the right side that gave Ottawa a 13-1 edge to that point in the period.
Benoit scored his sixth goal at 15:49 to finish a 3-on-2 break. Patrick Bordeleau took a cross-ice pass from Benoit and put a return feed around sprawled Senators left wing Milan Michalek to the former Ottawa defenseman, who beat Lehner with a shot from the slot to put the Avalanche up 1-0.
Duchene, whose pass sent Benoit away on the rush, got his second assist on Holden's power-play goal at 3:10 of the third period.
Nathan MacKinnon got his 30th assist of the season on Mitchell's goal at 17:02 of the third.
Colorado plays the second of its three-game Canada trip Tuesday against the Montreal Canadiens. That will be Roy's first game at Bell Centre as coach of the Avalanche.
"It's a big night for him, but he's going to play it off like it's not about him," Duchene said. "That's the way he is, and it won't be a distraction, by any means."
Erik Karlsson played his 300th game for Ottawa, which continues its three-game homestand Tuesday against the New York Rangers.