Just minutes after Wings forward Pavel Datsyuk scored on a brilliant individual effort to knot the game at 1, the Oilers cued the comeback.
First Sykora beat Red Wings starter Dominik Hasek stick-side on a breakaway, and then exactly two minutes later Lupul blazed in alone to score for the Oilers.
With the win the Oilers improved to 5-2, while Detroit slipped to 3-4-1.
It was the first meeting between the two clubs since the eighth-seeded Oilers knocked the Wings out in the first round of the Stanley Cup playoffs last season.
The game went scoreless through a sloppy first period, the best opportunity belonging to the Red Wings when Robert Lang missed a wide open net on a power play with just five minutes remaining in the initial frame.
The Oilers were the first to get on the board, 2:50 into the second, when defenceman Steve Staios' hard shot from the point caromed off a Wing and slipped by Hasek to put Edmonton ahead 1-0.
Edmonton had the bulk of the quality chances for the remainder of the second, but Hasek was able to shut the door, keeping it a 1-goal game entering the third.
Detroit was finally able to end Oiler goalie Dwayne Roloson's shutout bid with eight and half minutes left in the third when Pavel Datsyuk deked through the Oilers defence to tie the game before Sykora and Lupul responded.
The Oilers conclude a three-game home stand when they face the Phoenix Coyotes on Monday, while the Wings return to Detroit to take on San Jose on Wednesday.
Notes:Going into the game the Oilers were ranked 5th on the penalty kill and 17th on the power play, while the Red Wings have struggled in both areas, 26th with the man advantage and 28th short-handed ... Graham and LuAnn Snyder made their third stop on an RV trip to all 30 NHL cities to raise awareness for the Dan Snyder Memorial Arena to be built in Elmira, Ont., honouring the memory of their son Dan, who was a passenger in teammate Dany Heatley's Ferrari that crashed on Sept. 29, 2003 in Atlanta. Snyder died of his injuries.