Bishop stopped all 28 shots he faced as the Bolts beat the Red Wings for the first time since January 2003 and broke a seven-game losing streak on the road.
The game was scoreless until the third period when Tyler Johnson, J.T. Brown and Alex Killorn each scored for Tampa Bay.
Petr Mrazek made 24 saves for the Red Wings, who dropped a fifth straight overall and also fifth consecutive at Joe Louis Arena -- their longest home-ice skid since 1986.
Celebrity Families of 2014 [PHOTOS]