Aleksander Barkov also scored in the tiebreaker for Florida, which has won three of four overall and two in a row against the Red Wings.
Detroit lost for the sixth time this season when leading after two periods.
Florida scored twice in the third to tie the game.
Bjugstad evened it at 2 when he put the puck over Howard's shoulder with 5:22 left in the third. The Panthers cut it to 2-1 on a goal by Bergenheim exactly 5 minutes into the period. Dmitry Kulikov bounced a shot from the point that Bergenheim touched on the way to the net.
The Red Wings took a 2-0 lead in the second on Datsyuk's goal. Franzen slid a soft pass to Datsyuk to the left of the crease and he one-timed it into the net at 6:47. Franzen has 12 points in his last 10 games.
Datsyuk returned to the lineup after missing the last seven games with a concussion sustained Nov. 23 against Ottawa. Datsyuk has six goals and nine assists in 11 career games against the Panthers.
The Red Wings went ahead 1-0 on a power-play goal by Bertuzzi in the first. Franzen's shot from the left point was tipped by Datsyuk and blocked by Thomas before Bertuzzi poked in the rebound at 10:26.
The Red Wings had a goal disallowed early in the first due to goaltender interference. Jonathan Ericsson's slap shot from the left point found the corner of the net, but it was ruled that Daniel Cleary interfered.
NOTES: The Panthers played the Red Wings for the second time in five days. The Panthers won 2-1 on Saturday in Detroit. ... Red Wings C Stephen Weiss returned to Florida for the first time since he signed a five-year deal with Detroit in July. Weiss spent 11 years with the Panthers from 2002-2013. ... Boyes returned to the lineup after being a healthy scratch Sunday.