Ryan Smyth assisted on all three goals for the Oilers, who won their fourth straight game.
"Last year I was just happy to be here, and now just over a week it felt like a long time I've played," Dubnyk said. "I felt good about coming in."
Ryan O'Reilly scored in the final period and Semyon Varlamov made 16 stops for the Avalanche, who fell to 0-3 at home and have been outscored 9-2 in those games. They've won six of seven on the road, but their last regulation win at home came January 24, 2011 vs. St. Louis, a span of 17 games.
Barker, who was signed as a free agent by Edmonton on July 1, netted his first goal in an Oilers uniform while on the power play. With an interference penalty to Gabriel Landeskog about to expire, Barker skated through the left circle before depositing a backhand shot past Varlamov at the 7:55 mark of the second.
"It's tough to answer," Landeskog said of struggling at home. "It's the small details, like we're not getting the first goal. We're not getting that drive to the net and we're sometimes too careful with our chances."
Sutton also scored his first goal of the year nearly 6 1/2 minutes later, tipping a slot shot from Lennart Petrell for a 2-0 lead.
"It's a great feeling to finally get one," Sutton said. "We don't get many chances from the back end. It was great to help out."
O'Reilly notched a power play tally 5:42 into the third off a rebound, but the Oilers got that back just 27 seconds later when Horcoff was credited with his second goal of the season on a sharp angle shot from the right side.
Petrell notched his first career NHL point...This was Sutton's first goal in 61 games, dating to March 16, 2010...Including Friday, Colorado will play 14 of its next 18 games on home ice. Included in this stretch will be an eight- game homestand from November 18 to December 4, the longest continuous homestand in Avalanche history.