Anderson capped his effort with 15 saves in the final period as he improved to all-time 8-0-1 against the Panthers, for whom he played from 2006-09.
Turris tallied during a first-period power play and added another marker in the next frame for the Senators, who notched a second straight win to begin the lockout-shortened NHL season.
Jim O'Brien and Jakob Silfverberg also found the net in the victory.
Jose Theodore made 33 stops for the Panthers, who fell to 1-1-0.
Celebrity Families of 2014 [PHOTOS]