Khudobin played parts of two seasons with Minnesota before being dealt to the Boston organization and this was only his seventh NHL appearance.
The only goal against Khudobin came from Jason Spezza in the second period that brought the Senators within 2-1. Milan Lucic restored a two-goal lead for Boston with the only score of the third period.
Ottawa has dropped two in a row and will go into the final game of the season needing one point to ensure it will finish as the Eastern Conference's seventh seed in the first round of the playoffs. The Senators will enter that contest with a two-point lead over eighth-place Washington.
Ben Bishop took the loss while stopping 24 shots.
Rosie O'Donnell unveils nearly 50-pound weight loss
Putin thinks Obama would save him if he were drowning