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.
Members of Congress to keep receiving porn magazine
Justin Bieber crashes Drake Bell's album release party