Johan Franzen and Valtteri Filppula also scored for the Red Wings, who have captured five of their last six games and will continue their current six-game homestand on Saturday against Colorado.
Detroit goaltender Jimmy Howard finished with 23 saves.
Dustin Penner and Theo Peckham scored for the struggling Oilers, who have dropped four of their last five games and fell to 4-8-2 on the season. Nikolai Khabibulin yielded all six goals on 34 shots for Edmonton.
Franzen’s tally at 17:03 of the second period put the game out of reach at 5-0, but the goal was still significant. It was Franzen’s 100th career goal and his first since Oct. 28 against Phoenix. Franzen has scored all seven of his goals at Joe Louis Arena this season.
Mike Babcock used brand new second and third lines against the Oilers and it seemed to work well. The line of Filppula, Jiri Hudler and Franzen netted four points, with each line member at least picking up one assist. The same went for the line of Cleary, Todd Bertuzzi and Mike Modano, who picked up five points.