Ottawa won for the sixth time in seven games behind the work of a goaltender who was making just his 35th appearance over four years in the NHL.
Bishop's other shutout came two years ago when he was playing for St. Louis.
The teams played almost two full periods of scoreless hockey before Andre Benoit put the Senators in front on the power play with 49 seconds left in the middle stanza.
Guillaume Latendresse gave Ottawa some insurance with 7:44 to play and Colin Greening scored into the empty net with 2:02 remaining.
The Rangers fell for the third time in four games and dropped back into a tie for eighth place with the New York Islanders.
Henrik Lundqvist made 26 saves for the Rangers.
Celebrity Families of 2014 [PHOTOS]