With the game tied 1-1 near the midpoint of the third, a strong Columbus forecheck saw Jenner dig the puck free behind the Detroit cage and make his way into the right circle before rifling a wrister that sailed high past Petr Mrazek's short side to put the Blue Jackets on top at 10:08.
Dubinsky followed with his 13th of the season just 40 seconds later and Derek MacKenzie added an insurance marker at 15:48 to help Columbus claim its fifth victory in six games.
Sergei Bobrovsky stopped 39-of-40 shots for the Blue Jackets, who were able to bounce back from a scary incident in Monday's contest against Dallas that saw Stars' forward Rich Peverley suffer a "cardiac event" while on the bench early in the first period that caused the game to be postponed.
"(Bobrovsky) really held down the fort, kept us in the game and gave us an opportunity," Columbus head coach Todd Richards remarked. "We finished the game the right way."
With Detroit goaltender Jimmy Howard scratched just before game time due to the flu, Mrazek got his first start since Jan. 12 and made 33 saves.
Danny DeKeyser scored the lone goal for the Red Wings, who have lost two straight and four of their last five.
"It's a disappointing loss, but we've got to regroup and get back at it," Red Wings head coach Mike Babcock said. "There's no time to feel sorry for ourselves."
DeKeyser's heavy slapper from the high slot gave Detroit a 1-0 lead at 10:24 of the opening frame, but Columbus countered just under five minutes later following a strong effort in front of the net from Nick Foligno.
Nick Schultz fired a blast from the left point that Mrazek turned aside, but the rebound bounced into the slot and Foligno, despite being taken down by a defender, was able to sweep the puck into the net from his stomach to tie the tilt at 15:11.
After a scoreless second stanza, Columbus killed off its fifth penalty of the game just before Jenner's wicked wrister put the Blue Jackets on top.
Dubinsky scored off a nice feed from Matt Calvert at 10:48 and MacKenzie capped the scoring exactly five minutes later when he pounded one home from in front off a slick dish from Mark Letestu.