It was Tkachuk’s first hat trick this season and sixth in the NHL.
Tkachuk put Florida up 2-1 just 35 seconds into the third period when he set up to the left of the net and tipped Sam Reinhart’s slap shot from the left face-off circle. He completed the hat trick with an empty-net goal at 18:08.
The Panthers (31-29-3) had lost nine of their past 11 games, and ended a four-game road trip 1-3-0. Bobrovsky increased his career record against Detroit to 29-8-2 in 40 games.
Alex DeBrincat scored for the Red Wings (35-21-7), who have lost seven of their past 10 games (3-5-2). John Gibson made 20 saves.
Detroit captain Dylan Larkin left the game midway through the third period after losing an edge and having his right knee buckle following an awkward fall.
The teams play again in Florida on Tuesday.
Tkachuk gave the Panthers a 1-0 lead at 11:06 of the first period, burying a snap shot from the slot over Gibson’s glove under the bar off Carter Verhaeghe’s backhand pass from behind the net.
DeBrincat tied it 1-1 during a 5-on-3 power play at 10:56 of the second period. Patrick Kane got possession of the puck after a face-off win by Larkin in the right circle, skated to the high slot and sent a wrist shot that deflected off the glass behind the net. The puck bounced forward and DeBrincat batted it out of the air past Bobrovsky.