The Senators won their second in a row and moved two points in front of the New York Islanders for the No. 6 spot in the Eastern Conference standings.
Anderson, who has spent the last three seasons of his decade-long NHL career as Ottawa's No. 1 goaltender, has 22 shutouts overall.
The game's two goals came less than 4 minutes apart in the second period with Jean-Gabriel Pageau and Milan Michalek scoring for the Senators.
Those two goals came on a total of just 11 shots faced by Martin Brodeur. The Devils remained four points out of a playoff position.