Mattias Ekholm scored, and Skinner made 29 saves for the Oilers (49-23-9), who have won eight in a row to extend their point streak to 14 games (13-0-1).
Edmonton is second in the Pacific Division, two points behind the Vegas Golden Knights, who won 4-1 against the Seattle Kraken on Tuesday. Each team has one game remaining; the Oilers host the San Jose Sharks on Thursday, when the Golden Knights visit the Kraken.
"That was a heck of a game. Fans got their money's worth," Edmonton coach Jay Woodcroft said. "I thought it was well played. It wasn't run-and-gun and taking needless chances. It was a workmanlike win. Nobody got impatient with the way the game was being checked. In the end, we found the key play at the right moment, but I think the more games we play like that heading into the playoffs, the better it is for us because we call these dress rehearsals.
"We've got one left, and we're pushing to finish as high as we possibly can. We came into this building against the Stanley Cup champs. This is how we expected to play, and we went out and we executed."
Ben Meyers scored, and Alexandar Georgiev made 38 saves for the Avalanche (49-24-7), who had won five straight.
Colorado moved into first place in the Central Division, one point ahead of the Dallas Stars with two games remaining, and clinched home-ice advantage for the first round of the Stanley Cup Playoffs.
"I thought it was good hockey. It's a close hockey game. You expect it to be," Avalanche coach Jared Bednar said. "We played our game to the bitter end and did a nice job. We killed some big penalties. We had some opportunities on the power play."
Meyers was credited with a goal to make it 1-0 when Oilers forward Nick Bjugstad dove to sweep the puck away from him and it caromed off the skate of defenseman Philip Broberg at 4:52 of the first period.
"It was kind of a tough play," Skinner said. "It's just a kind of crazy broken play, went off a stick, another stick, went off a skate, and then right when it went off the skate, I moved my pad up just that second. It's a game of inches. It's about what you do after that, and 'Eks' scored right away. And I think that's a huge bounce- back just to be able to get that momentum shift."