The Red Wings usually outshoot their opponents, especially at home, but the Avalanche peppered Detroit goalie Jimmy Howard with 38 shots.
Brandon Yip then scored in the sixth round of the shootout to give Colorado a 5-4 victory over Detroit on Tuesday night.
Peter Budaj faced only 28 shots from the Red Wings through overtime. The Avalanche held a 23-13 shots edge through two periods.
"To get that many shots in this building, it was a real good win for us," Colorado coach Joe Sacco said.
"We did a good job of keeping it simple and outworking them," Jones said.
Budaj stopped 24 shots.
"They didn't stop. Even when they got down they kept coming hard," Howard said. "They don't quit. They're a hardworking team, they're very fast through the neutral zone."
Jones' second goal of the game, on a backhanded shot from the slot, tied the game with 8:24 left in the third.
Eaves' short-handed goal 7:52 into the third period gave the Red Wings a 4-3 lead. He completed a 2-on-1 by converting Darren Helm's pass after John-Michael Liles couldn't hold the puck in at the Red Wings' blue line. It was Eaves' first goal.
"It [hurts] when you shoot yourself in the foot and let in a shorty," Jones said.
Winnik tied the game at 3 with his first goal, scored 4:43 into the third period when he beat Howard from the bottom of the right circle.
O'Reilly's goal with 48 seconds left in the second cut the Avalanche's deficit to 3-2. His slap shot from the left circle beat Howard after the Red Wings' Ruslan Salei and Jiri Hudler couldn't control the puck at the Colorado blue line.
"That goal got us back into the game," Sacco said.
Detroit coach Mike Babcock lamented all the errors made by his club.
"Their first three [goals] were all turnovers. If I'm not mistaken, even the fourth one was a turnover. You can't turn the puck over," he said. "They did a good job of not turning the puck over. They went north-south and we went more east-west and when you do that you get more turnovers ... and it ends up in your net."
Second-period goals by Datsyuk and Franzen gave Detroit a 3-1 lead.
Datsyuk's 200th NHL goal, which came on the power play 2:35 into the second, made it 2-1. He tipped in Henrik Zetterberg's slap pass for his second goal of the season.
Franzen netted his second of the game and third of the season with 6:02 left in the second period with a shot from the bottom of the right circle.
Franzen opened the scoring 2:34 into the game. Jones tied it with 3:04 left in the first period.
Veteran Detroit F Kirk Maltby announced his retirement before the game. Maltby, 37, played 16 seasons in the NHL and 14 with the Red Wings. He will remain with the organization as a pro scout. ... Red Wings D Brian Rafalski will be out 3-4 weeks after undergoing arthroscopic knee surgery. Rafalski won't be placed on the injured list. The Red Wings recalled D Doug Janik from Grand Rapids (AHL). ... Detroit C Kris Draper (groin) was placed on the short-term injured list. ... With an assist on Winnik's goal, Colorado captain Adam Foote has 253 points with the Avalanche, tying him with Sandis Ozolinsh as the highest-scoring defenseman in franchise history.