Eberle scored twice in Edmonton's five-goal third period and also added an assist. Zack Kassian and Leon Draisaitl also scored in the rally that moved Edmonton into a tie with Anaheim for second in the Pacific Division with 89 points.
The Oilers tied it early in the third and then scored three times in the final 2:11. Caggiula beat Jeremy Smith to give Edmonton a 5-4 lead, Eberle added to it and Draisaitl scored into an empty net in the final minute to seal it.
The Avalanche got early goals from Rantanen and Compher to take a 2-0 lead but Edmonton tied it with goals by Sekera and Lucic 57 seconds apart spanning the first and second periods.
Rantanen broke the tie at 4:22 of the second with his second of the night, and Bourque's 12th of the season at 17:45 made it 4-2.
Talbot gave way to Brossoit to start the third, but it was Edmonton's offense that sparked the comeback. Kassian started it when he snuck behind Smith to knock in the puck sitting in front of the empty net at 2:44 of the third.
Eberle, who assisted on Lucic's goal, tied it at 4:34 with his 15th of the season.
Edmonton C Connor McDavid increased his lead in the scoring race with two assists. He has 87 points, six ahead of Pittsburgh's Sidney Crosby. ... The Avalanche have been outscored 22-10 during their four-game losing streak and 28-15 in the last seven games. ... Colorado C Joe Colborne finished with two assists.
Oilers: Host the Avalanche on Saturday night to complete the home-and-home set.