Sam Gagner, Magnus Paajarvi and Ryan Nugent-Hopkins also scored for the Oilers, who went 3-4-2 on a nine-game road trip.
Dubnyk was in top form even after leaving early Sunday at Chicago with a neck injury following a collision with a teammate. He showed no lingering effects, stopping everything thrown his way for his fifth NHL shutout.
Colorado nearly scored on Dubnyk early in the third period, but Jan Hejda's goal was disallowed when Gabriel Landeskog was called for goaltender interference.
Horcoff is steadily rounding back into scoring shape after missing 15 games with a broken knuckle on his right hand. The captain scored his third goal of the season midway through the opening period — more than enough offence for Dubnyk.
The Avs were bottled up as they concluded a three-game homestand. They began by halting the Blackhawks' NHL record streak of earning at least one point in the first 24 games and then knocked off San Jose on Matt Duchene's goal just before the horn sounded to end overtime.
This was Colorado's first loss at home since Feb. 11.
The Oilers solved Semyon Varlamov, who has been hard to beat at home, where he is 8-3-1. Only Jimmy Howard of Detroit and Henrik Lundqvist of the New York Rangers have more home wins this season with nine each.
Soon after Colorado's goal was nullified, Nugent-Hopkins scored on a power play to seal the Oilers' second straight win.
Paajarvi extended Edmonton's lead to 3-0 midway through the second period when he caught the Avalanche in a shift change. The forward zipped down the left boards and lined a shot at Varlamov, the puck bouncing high into the air. Paajarvi patiently waited for it to come down before swatting it in.
Edmonton not only took advantage of favourable bounces, but defenders falling down, too.
Horcoff had an easy path to the net after Landeskog tripped trying to thwart the play. Horcoff simply skated in on Varlamov and lined a shot between the goalie's pads.
Five minutes later, Gagner added his team-leading 10th goal of the season when he slid across the crease with Varlamov on the ice and knocked in a loose puck.
Colorado forward P.A. Parenteau had his career-best, six-game point streak end.
NOTES: Avalanche F Milan Hejduk missed a fifth game with a torso injury, but he could soon return to practice. ... Avs D Tyson Barrie was reassigned to Lake Erie of the AHL before the game. ... Edmonton forwards Ales Hemsky and Taylor Hall both had two assists. Eight Oilers had at least one point.