Anderson, who picked up his second shutout of the season, was especially sharp in the third period with the Sabres pressing for the tie as the Senators (7-4-2) snapped a mini two-game slide.
Ryan Miller made 29 saves in taking the loss for Buffalo (5-8-1).
Scoreless after the first period, the Senators had a number of great chances in the second but couldn't beat Miller until Karlsson moved in shorthanded and blasted a shot just over the Buffalo goalie's left pad at 15:20.
Condra then doubled the Ottawa just 1:54 later off, banging home a loose puck off a scramble in front Miller's goal.
Daniel Alfredsson had a great chance to open the scoring for the Senators on the power play prior to the two-goal barrage, but the Ottawa captain's one-timer missed the net with Miller at his mercy.
Buffalo had a chance to get back in the game midway though the third when Ottawa's Jim O'Brien went off for holding and Kyle Turris was whistled for high sticking to set up a two-man advantage for 14 seconds. But Anderson and the Senators penalty killers did the job against a Sabres power play that finished the night 0-for-4.
Ottawa's Jakob Silfverberg had a chance to stretch the Senators' lead to three on a power play later in the period, but Miller sprawled to make a diving save at the side of the Buffalo net.
The Sabres held a 13-7 shot advantage in the first period but couldn't solve Anderson.
Despite the win, Ottawa finished the night a disappointing 0-for-8 on the power play.
Notes: Ottawa visits Pittsburgh on Wednesday, while Buffalo is home to Boston on Friday. ... Attendance at Scotiabank Place was 18,429.