The Sabres build a comfortable lead, his teammates play tight defense and Miller only faces a few shots.
"We stayed ready," Miller said. "We knew Atlanta had some shooters and that they would get their chances later. We dictated the pace."
"It was a great effort," said Miller, last season's Vezina Trophy winner and an Olympic star. "We got ourselves going early. That was the big difference."
Tobias Enstrom scored for Atlanta. The Thrashers, outshot 42-18, had won two straight.
Myers gave the Sabres a 2-0 lead six seconds into a power play and 1:30 into the second with a slap shot from the blue line. McCormick scored 1:04 later on a short wrister after goalie Chris Mason lost control of a rebound.
"Buffalo is a hard working team, which is somewhat of the identity we want to take on, and we didn't do that tonight," Mason said. "Neutral-zone issues -- teams like Buffalo will keep coming at you and take advantage of your mistakes."
Atlanta cut it to 3-1 on defenseman Enstrom's second goal, a slap shot on the power play, but the Thrashers' offense was otherwise dismal.
"Attention to detail was almost nonexistent," Atlanta coach Craig Ramsay said. "We had a couple of days off, we had two good practices and there's no reason for them not to come and be able to play."
Vanek scored on a breakaway with 9:35 left in the third.
Ennis opened the scoring in the first period with a wrist shot.
"I think from start to finish, we were on top of the puck," Buffalo coach Lindy Ruff said. "It was nice to see some opportunities go in."
After going 1-12-3 in their previous 16 games at Philips Arena, the Sabres pressured the Atlanta defense all night, a formula they've used to outshoot opponents 119-65 in three road games.
"We didn't do anything to make [Miller] work," Mason said. "We didn't test him."
Buffalo didn't immediately list the condition of Montador, who blocked his 21st shot of the season. He began the game tied with Chicago's Nick Boynton for the NHL lead with 20.
Defenseman Chris Butler added two assists for the Sabres.
Sabres center Derek Roy assisted on Myers' goal for his 27th point in 23 career games against Atlanta. ... Ennis has five points this season. ... Buffalo right winger Jason Pominville (concussion) missed his fourth straight game. ... Thrashers defenseman Zach Bogosian (shoulder) missed his third in a row. ... Sabres defenseman Shaone Morrisonn (groin) has been out three straight. ... Atlanta defenseman Niclas Bergfors, the central player acquired in the deal that sent Ilya Kovalchuk to the New Jersey Devils last season, was a healthy scratch for the second time in three games.