Playing for the second time in as many nights, the Sabres found enough energy late to extend their winning streak to three games for the first time since March 7-10.
Kalinin and Mair both scored from sharp angles against Sebastien Charpentier, who made his NHL debut here in April, stopping 38 shots in a 3-1 win. Playing for the injured Olaf Kolzig, he made 40 saves in a losing effort.
After Jaromir Jagr's go-ahead goal 2:51 into the third period, the Sabres dominated the final 17 minutes, holding a 17-0 advantage in shots.
Buffalo outshot the Capitals, 22-5, in the final period and 44-25 for the game.
Kalinin tied it with 3:11 remaining, one-timing Chris Gratton's feed under Charpentier's right pad from the bottom of the left faceoff circle for his third goal of the season.
Mair then got off a quick one-timer from the right circle, putting Taylor Pyatt's pass from the goal line through Charpentier's pads for his second goal of the season.
Miroslav Satan had a goal and an assist for Buffalo, which improved to 3-1-1 in its last five home games since its new ownership group was approved.
Peter Bondra scored a shorthanded goal for the Capitals, who were coming off Friday night's 7-6 overtime win over Atlanta. They have allowed 22 goals in their last five games.