Roy scored 3:35 into overtime and Miller made 34 saves to lead Buffalo to a 3-2 win over the Toronto Maple Leafs.
"Ryan's our rock out there, he made some huge saves and we finally got our act together in the third period," Roy said after the Sabres came back from a 2-1 deficit.
The Sabres have surrendered two or fewer goals in 13 of their past 15 games. They only allowed three goals in the other two outings.
"It was a hard-fought game tonight," Miller said. "We came back and played a tight third period. Even though we only had a couple of chances, we made one count and we got to overtime."
After winning an offensive-zone faceoff and an ensuing race to the loose puck, Sabres center Jochen Hecht passed to Roy in front, who deked and then went to his backhand to beat Maple Leafs goalie Jonas Gustavsson.
"[Steve] Montador made a great play and Hecht made a great pass," Roy said. "I just waited for a half-second for [Gustavsson] to make a move, and then I went upstairs."
Hecht also scored for Buffalo at 12:59 of the third period to tie the game at 2-2. Nathan Paetsch, with his first goal of the season, opened the scoring in the first period, while Montador added two assists.
"I'm happy when anybody scores," Sabres coach Lindy Ruff said. "Whether it's Hecht or anyone else, I'm just happy.
"There weren't a lot of pretty goals tonight. Derek's was pretty, but that was about it."
The win was the sixth in eight games for the Northeast Division-leading Sabres.
"We've improved this year," Miller said. "We've been in some tight games and been able to come through."
Rookie forward Viktor Stalberg, with his second goal in three games since being recalled from the American Hockey League, and Ian White replied for Toronto. The Maple Leafs lost for the third time in four games.
"Toronto was throwing the puck around, going back door and crashing the net hard," Roy said. "They were doing all the things they had to do. I thought they played well."
Once again, the Sabres relied heavily on Miller, who leads the NHL in goals-against average and save percentage and is the leading candidate to be the United States' starting goalie at the Olympics.
He stopped every puck he saw as both Stalberg's and White's goals came on crease-crashing deflections. The win was Miller's ninth in his past 10 games against the Maple Leafs.
"They were driving hard to the net, and that's what happens sometimes," Miller said. "They did a good job of creating traffic and coming at me hard tonight. I sort of figured that it was coming, especially after they knocked me over a few times in the first few minutes."
Gustavsson, coming off the first shutout of his career in a 2-0 win over Boston on Saturday, stopped 27 of 30 shots.
The Sabres led 1-0 after a frantic first period in which both teams fired 13 shots and had several good scoring chances. Gustavsson made a nice save on Buffalo left winger Clarke MacArthur in the early going, while Miller denied Leafs right wing Lee Stempniak on a short-handed breakaway in the later stages of the opening period.
Stalberg and White scored goals in the second period to give Toronto a 2-1 edge heading into the third, but the Leafs couldn't fend off the Sabres -- or get another puck past Miller.
Hecht got the Sabres even at 12:59 of the third period when he collected a loose puck in the slot and lifted a backhand over Gustavsson to make it 2-2 and set the stage for overtime.
Paetsch, skating in just his eighth game of the season, opened the scoring at 6:11 of the first period. Buffalo left wing Matt Ellis won a battle along the boards and slid the puck to Paetsch, who swept a low wrist shot that beat Gustavsson through the legs.
The goal was Paetsch's first since Feb. 6, 2009, and just his seventh in 154 career NHL games.
Buffalo was 0 for 1 on the power play, while Toronto didn't have a single man advantage. ... Buffalo left winger and leading goal scorer Thomas Vanek sat out a second consecutive game nursing an abdominal injury.