Anderson has allowed an average of 3.4 goals per game this season, but he shut down the Sabres after Tyler Ennis scored on the power play with 2:21 to go in the opening stanza.
The goal by Ennis created a 1-1 tie which was broken when Zack Smith delivered the game-winner 6:39 into the second.
A deflection by Bobby Ryan at the 9:22 mark of the first gave the Senators the early lead.
Buffalo was trying to win back-to-back games for the first time this season. Instead, the Sabers suffered their 25th loss, most in the NHL.
The loss went to Ryan Miller, who made 30 saves.