Bogosian was sent off for elbowing when he brought up his right arm before delivering against the boards on Kaleta, who scored Buffalo's goal in regulation.
"Penalties played a big role," Kaleta said. "We finally got a power play that paid off for us."
With the Thrashers down to only three skaters, the Sabres had plenty of room to operate. Tim Connolly guided the power play from the center of the ice, just inside the blue line, and slid a pass to Roy all alone at the top of the right circle. He ripped off his 11th goal of the season, a one-timer over Ondrej Pavelec's left shoulder.
Bogosian didn't complain much about the penalty.
"It all happened so fast," he said. "I really don't know. I'm not the ref, so I don't make the calls."
Buffalo was coming off a 4-3 shootout loss to Colorado on Saturday, snapping a six-game winning streak. Ryan Miller made 32 saves for the Sabres, improving his record to 26-8-3.
At the start of overtime, the Thrashers had to kill off the final 50 seconds of a holding penalty against Christoph Schubert. The teams played less than a minute at even strength before Bogosian was sent off.
"It's tough when you're short-handed the first few minutes of overtime," Atlanta coach John Anderson said. "They're going to get a few good scoring chances."
Ilya Kovalchuk scored his 27th goal for Atlanta, which was hoping to follow up its first regulation win since Nov. 30 after blowing out Ottawa 6-1 on Tuesday. The Thrashers have gone exactly a month since putting together consecutive victories, their last winning streak a modest two-game stretch that ended on Dec. 14.
"Out of the two teams that could afford the point the most, it wasn't us," Anderson said. "We need every point we can get right now. We're not getting out share of breaks right now, but I know if we keep playing hard and as good as we are, good things will happen. The hockey world will even up."
Kaleta put the Sabres ahead 3 minutes into the second period, taking advantage of a fortuitous bounce after an errant shot by teammate Toni Lydman.
The Buffalo defenseman missed the net with a shot from the point, but the puck ricocheted off the boards and straight to Kaleta standing on the opposite side of the crease. As Pavelec scrambled to get back into position, Kaleta flipped a perfectly placed shot just under the crossbar for his seventh goal.
The Thrashers, after failing to convert on their first five power plays, finally took advantage when they were a man-up the sixth time. Slava Kozlov guided a pass to Kovalchuk breaking in from the left point, and the Atlanta star had time to settle it on his stick, move inside the faceoff circle and rip one over Miller's glove.
The Buffalo goalie probably had trouble getting a good look at it with defenseman Steve Montador and Atlanta's Bryan Little clogging things up in front of the net.
"We put ourselves in a touch spot, but we bounced back with some good penalty killing," Miller said. "We stuck with it. We did a good job penalty killing. We battled hard."
The teams played before another sparse crowd at Philips Arena. The announced turnout of 11,313 was the ninth time in 22 home games that Atlanta has failed to draw 12,000 fans. The Thrashers rank 28th in the NHL in attendance; the New York Islanders and Phoenix Coyotes are the only teams lower.
"This is a good building to play in," Roy said. "It's kind of quiet."
NOTES: The Sabres scratched left wing Matt Ellis and defensemen Nathan Paetsch and Andrej Sekera. ... Center Todd White took part in the morning skate but didn't dress for Atlanta after hurting his right leg in the previous game against Ottawa. The Thrashers also sat defensemen Mark Popovic and Anssi Salmela. ... Tobias Enstrom also picked up an assist on Kovalchuk's goal, the 107th point of his Atlanta career. That tied Enstrom with Yannick Tremblay as the highest-scoring defenseman in Thrashers' history.