Matt Duchene had two assists for the Avalanche (44-19-5), who have won three of four and seven of their past nine games.
Robin Lehner made his second straight start for the Senators (28-26-13) since Craig Anderson was injured last week in a loss to the Nashville Predators. Lehner made 19 saves but had no chance on any of the goals he allowed.
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 forward 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 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 in the game.
Following a scoreless opening period, Ottawa held a heavy edge in play over the second 20 minutes.
Ottawa outshot the Avalanche 20-8 in the second period but it was former Senator Andre Benoit that scored the period's only goal and gave Colorado a 1-0 lead in the process.
The Avalanche broke out three-on-one late in the period and after receiving a drop pass from Patrick Bordeleau, Benoit moved into the slot and put a shot over the should of Lehner.
Benoit was a fan favourite 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.
Notes: Matt Kassian, Patrick Wiercioch and Craig Anderson were scratches Sunday for the Senators. Scratches for the Avalanche were P.A. Parenteau, Paul Stastny, Paul Carey, Ryan Wilson and Reto Berra…Senators defenceman Erik Karlsson played his 300th NHL game on Sunday. Forward Kyle Turris played in his 300th game Saturday in the Senator's loss to Montreal…The last time the Avalanche recorded 44 wins in a season was back in 2007-08…The Avalanche are the only team in the NH to sore at least one goal in every game this season.