Trailing 4-1 late in the second period, the Oilers reeled off the next five goals to pull out only their second win of the month.
Ryan Nugent-Hopkins and Ales Hemsky scored in the second period, cutting Edmonton's deficit to one, and Jordan Eberle notched the equalizer 9 minutes into the third with a power-play goal that set up Paajarvi's decisive goal with 1:34 remaining.
Eberle finished with two goals and an assist, Hemsky scored twice and Taylor Hall had three assists for the Oilers.
Devan Dubnyk started in goal for Edmonton but was chased after yielding three goals on 12 shots. Nikolai Khabibulin relieved and earned the win, stopping 17-of-18 the rest of the way.
Colorado's Semyon Varlamov faced 55 shots -- the most ever allowed by the Avalanche in a regular-season game -- stopping 50 of them as the Avs fell for the fourth time in five games.
Matt Duchesne and Jamie McGinn each logged a goal and two assists for Colorado.