Jimmy Howard had 33 saves, and Gustav Nyquist had a goal for the Red Wings, who are locked in a tight fight for a postseason spot.
"We needed these points. We have a tough situation in the fight for the playoffs, and we're happy we finished this way," Datsyuk said.
It wasn't easy. Detroit lost in Phoenix on Thursday and had to play at altitude against a struggling but rested Colorado team. Fatigue showed when the Avalanche held a 16-6 advantage in shots in the third period.
"We let off the gas a little bit there in the third but I think that had a lot to do with it being the second game in two nights," Howard said. "The key is we found a way to get the two points and a much-needed two points."
P.A. Parenteau and Mark Olver scored for Colorado, which gave Detroit all it could handle before losing for the 11th time in 13 games.
The rivalry that blossomed between these teams in 1996 has lost steam with Colorado's string of nonplayoff seasons. Still, the Red Wings' presence in Denver always adds a charge even if neither team looks like those that combined to win five Stanley Cup titles from 1996 to 2002.
"There were some positives again. We've played some good games lately," Parenteau said. "We're not getting the results."
The Red Wings went into Friday having lost three of four. They slipped to seventh place, one point ahead of St. Louis, which has played two fewer games. Detroit is a perennial top seed in the postseason but is in danger of missing the playoffs for the first time since 1990.
However, in this lockout-shortened season, things change in a hurry. A loss to Colorado would have moved Detroit to eighth in the conference.
The Avalanche have been reduced to the spoiler role for the third straight season. Colorado is last in the NHL in points and is looking at a high draft pick for the fourth time in five seasons.
"It's just frustrating right now," said Giguere, who made 28 saves. "We can all feel the pressure, and it's just unfortunate."
Despite the different directions, this game was close. Detroit took a 1-0 lead on Datsyuk's power-play goal midway through the first period -- his team-leading 12th goal of the season.
Colorado tied it when Olver scored on a breakaway at 11:36, but Nyquist gave the Red Wings the lead back with his second goal 13 seconds later.
"It bobbled in the middle, and the puck kind of came right to me. I just tried to fake the shot, have him go down and tuck it in short side," Nyquist said.
It stayed that way until the third, when Colorado came out charging. The pressure paid off when Parenteau tipped in a pass from Jamie McGinn at 6:29 to tie it 2-all.
The Avalanche continued to dominate in the third and held a 14-1 advantage in shots before Tyson Barrie took a penalty at 14:16. The Red Wings couldn't take advantage of the power play, and the game went into overtime.
"It was very obvious we were running out of gas big time, but our guys hung with it. We got some good goaltending and we found a way to get it done," Detroit coach Mike Babcock said. "It was one of those nights on your schedule you think it's going to be a tough one."
The Red Wings can help themselves when they play the Blues in Detroit on Monday. A win would give them separation in the final stretch of the shortened season.
"It's a big game for us," Babcock said. "St. Louis has two games in hand. It's a big game plus we always have fun playing against them."
Detroit D Kyle Quincey returned after sitting out 10 games because of facial fractures sustained March 15 against Edmonton. ... Zetterberg earned his 399th career assist. ... Olver's goal was his first point in eight games. He had a goal and assist against Dallas on March 20.
Copyright by STATS LLC and The Associated Press
DENVER, CO - APRIL 5: Niklas Kronwall #55 of the Detroit Red Wings warms up prior to a game against the Colorado...