Butler, who has five goals in his past five games, scored midway through the first. He added his second of the game midway through the second to give Ottawa its second two-goal lead.
Jason Spezza had a goal and two assists and Ryan Shannon had a goal and an assist. Milan Michalek also scored for the Senators, who had not won at Scotiabank Place in nearly two months.
Ottawa, which is last in the Eastern Conference with 49 points, had gone 0-7-3 at home following a win over Pittsburgh on Dec. 26.
Anderson won his second start in a row since the Senators acquired him from Colorado on Friday in a trade for goalie Brian Elliott. The former Panthers goalie made 47 saves in his Ottawa debut on Saturday night, turning aside three shootout attempts to secure a 1-0 win in Toronto for his first shutout of the season.
Chris Higgins scored his 11th goal for Florida, which has lost four of five. Scott Clemmensen stopped 29 shots.
Senators right wing Chris Neil left midway through the second with a lower-body injury. He did not return.
Butler gave Ottawa a 1-0 lead 11:13 in when his backhand went in off Panthers defenseman Mike Weaver.
Shannon made it 2-0 when he beat Clemmensen for his sixth goal of the season early in the second.
Clemmensen got an assist when Higgins scored at 4:18 to draw Florida within 2-1.
Butler restored the Senators' two-goal lead with an unassisted effort at 10:38.
Michalek made it 4-1 with his 15th goal 16:49 into the third. Spezza scored Ottawa's fifth goal, his 11th, at 18:38.
NOTES: Clemmensen fell to 3-1 against the Senators. ... Anderson went 89 minutes, 18 seconds into his Ottawa career before allowing his first goal. ... The Senators are 10-16-5 at home.