Trailing 3-1 heading into the third period, Edmonton scored four times in the final 20 minutes on a pair of goals from Ryan Smyth, and single goals from Marc-Andre Bergeron and Ethan Moreau.
Edmonton's Shawn Horcoff tied a team record with four assists to leave the Red Wings winless on a three-game swing through Western Canada.
Brendan Shanahan brought the Red Wings to 5-4 with a power-play goal, and Steve Yzerman tied it with his second of the season with 2:18 left in regulation.
Ales Hemsky had a power-play goal in the first period for Edmonton, which will play six of eight at home. The Oilers recently completed a season-high, seven-game road trip.
Mikael Samuelsson, Pavel Datsyuk, and Johan Franzen also scored for Detroit (15-4-2), which lost at Vancouver on Sunday and in Calgary on Wednesday.
Hemsky converted Chris Pronger's pass to the side of the net for a one-timer off a two-man advantage in the first period.
Samuelsson intercepted a long lead pass from Pronger and ripped a shot past Jussi Markkanen just under two minutes later to tie it 1-1 despite Detroit holding a 10-5 shots advantage.
Detroit went ahead 3-1 after Datsyuk, on a power play, and Franzen scored back-to-back goals from the high slot in the second period.
Markkanen, starting for the 15th time in 16 games, made 23 stops for his ninth win for Edmonton. ... The Oilers were 3-for-8 on the power play. ... Canadian Champ Car driver Alex Tagliani drive a souped-up Zamboni around the ice during the second intermission.