Howard has 13 shutouts in a seven-year career. Six of those came last season.
After a scoreless first period, Jakub Kindl produced his second goal of the season 3:16 into the middle stanza.
Cory Emmerton scored midway through the second and Justin Abdelkader had an empty-net goal with 1:10 left in the third. It was his first of the season.
Detroit has won five of its last seven games and earned a point in one of the two losses. The Red Wings have defeated the Oilers in each of their last seven visits to Detroit.
Devan Dubnyk gave up two goals on 25 shots. The Oilers fell to 1-3-2 on a nine-game road trip.