DENVER -- Shane Prince was getting frustrated it was taking so long to get his first NHL goal.

He took care of the milestone early Wednesday and helped the Ottawa Senators to a nail-biting victory.

The left winger scored his first two NHL goals and also had an assist, center Zack Smith had a goal and an assist and Ottawa survived a third-period rally to beat the Colorado Avalanche 5-3 on Wednesday night.

Prince had played 12 of his 14 career games this season without recording an NHL point but made up for it against the Avalanche.

"It was good to get the monkey off my back," he said. "To keep on a streak without a goal is one of the hardest things to go through as a professional athlete. Your whole world in life is upside down until you get that one."

Center Kyle Turris and Mika Zibanejad also had a goal and an assist and goaltender Craig Anderson had 40 saves, 20 in the third period, against his former team as the Senators won their fourth straight.

Center Nathan MacKinnon and left winger Gabriel Landeskog had a goal and an assist and right winger Chris Wagner scored his first NHL goal for Colorado.

"It's the best league in the world and scoring in it is just a blessing but obviously you want to get the win there," Wagner said.

The Avalanche nearly came back in the third to earn at least a point in their first home game in 19 days. Landeskog cut the lead to 4-2 with a power-play goal at 10:50, and MacKinnon got the Avalanche closer with his 10th of the season 1:36 later.

Goalie Reto Berra came off for an extra skater with 2:03 remaining. Colorado had chances to tie but Zibanejad scored into the empty net to seal the win.

"We had the puck in certain areas with the game in hand and tried to do stuff that just didn't make any sense," Ottawa coach Dave Cameron said. "They came back and they scored and got some momentum, got the next one and the heat was turned up. We hung on. Huge two points."

Prince's first goal, at 5:54 of the first, snuck through goalie Semyon Varlamov's pads and crept over the goal line to make it 1-0.

He didn't have to wait long for his second. He came down the slot and knocked in a centering pass from Smith just 3:07 later.

"I haven't been able to get a bounce so far this year," Prince said. "So my mindset was to throw everything on net and shoot every chance I get. Sure enough, first shift I get a little squeaker there and the floodgates open."

The Avalanche cut the lead in half when Wagner skated across the front of the net and tipped in a loose puck at 10:36. It was the first point of his career and came 10 days after Colorado claimed him off waivers from Anaheim.

The Senators responded at the start of the second period. Left winger Mike Hoffman sent a pass to Turris in the slot and he beat Varlamov on the short side 1:48 into the period. It was his team-leading 11th of the season.

Backup Reto Berra came on for Varlamov, who gave up three goals on just 15 shots.

"That was a bad goal, the first one, coming off a seven-game road trip," Avalanche coach Patrick Roy said of Varlamov. "When I saw the first one going in I said, 'C'mon Varly. That can't happen.' That was not a dangerous shot at all. It was coming from the board and it really hurt us a lot. It took some momentum off of our game."

The Avalanche had chances to pull closer, but Landeskog hit the left post with a snap shot at 12:25 of the second.

Smith gave the Senators breathing room with his fifth goal of the season at 18:13 of the second.

NOTES: Avalanche RW Alex Tanguay (knee) has begun skating but is expected to miss at least three more weeks. Tanguay hasn't played since sustaining the injury Nov. 6 against the New York Rangers. ... Ottawa G Andrew Hammond is on injured reserve with a head injury. Rookie Chris Driedger, recalled from Birmingham of the AHL on Monday, served as Craig Anderson's backup for the second straight night. ... Avalanche C John Mitchell missed his fifth consecutive game with an oblique injury. He missed four games early in November with the same injury. ... Senators D Patrick Wiercioch missed his third game in a row due to an upper-body injury.