"It was a big weekend for us and we lose both games," Senators captain Jason Spezza said. "We played good, but it's a different way to lose every night and results are the only thing that matter right now.
"We didn't turn the puck over much, we created a lot, but again, it just wasn't enough to win the game and it's unacceptable."
Varlamov was 6 seconds away from his second shutout of the season and 13th of his career until Mika Zibanejad scored for the Senators.
Matt Duchene had two assists for the Avalanche, who have won three of four and seven of their last nine.
"Response to the game (Saturday) was positive," Senators coach Paul MacLean said. "A lot of the statistical things were positive, but at the end of the day, it's the score that matters and we gave up three goals and only scored one.
"We created opportunities to score, but I don't think we got to their net as hard as we could have and we missed the net a number of times."
Nursing a 1-0 lead heading into the third period, the Avalanche were awarded their first and only power play of the game when Ottawa's Chris Neil closed his hand on the puck and was called for delay of game.
Duchene took a shot during the man advantage that Lehner stopped, but the rebound went right to Holden who was alone at the side of the net and scored at 3:10.
"The power play was sharp again," Avalanche coach Patrick Roy said. "We had only one opportunity, but scored a very important goal for us."
The Senators pressed throughout the period, but the game was virtually over when Mitchell beat Lehner from in tight with less than three minutes to go.
Following a scoreless opening period, Ottawa held a heavy edge in play over the second 20 minutes -- but the Senators couldn't solve Varlamov.
"He was very solid and he made some very key saves," Roy said of Varlamov. "I thought we had too many turnovers in that second period. Our goalie was without a doubt the first star of the game."
Ottawa outshot the Avalanche 20-8 in the second period, but it was former Senator Andre Benoit who scored the period's only goal and gave Colorado a 1-0 lead in the process.
The Avalanche broke out 3-on-1 late in the period and, after receiving a drop pass from Patrick Bordeleau, Benoit moved into the slot and put a shot over Lehner's shoulder.
Benoit was a fan favorite in Ottawa despite playing just 41 games for the Senators over two seasons. He has played in 66 of Colorado's 68 games this season. He also has nine goals in 107 career games, but four of those have come in his last nine games.
"It's always fun to score against an old team and I had lots of family and friends here," said Benoit, who is from St. Albert, about 30 minutes from Ottawa. "Hopefully they keep going in. It was a big game and we were able to get a win. We have to keep this going now."