Daniel Briere added a goal and an assist, and Jason Pominville also scored for the Sabres, who have won three straight and four of their last five.
Glen Metropolit scored for the Thrashers, who were denied in their second bid this month to win six straight games for the first time in franchise at history.
Miller was making his third straight start, and has allowed five goals in those games. He got help in the first period when Atlanta forward Jean-Pierre Vigier shot wide on a short-handed, breakaway attempt.
The Thrashers defeated Buffalo 5-4 in a shootout in October, snapping the Sabres' NHL record-tying 10-game winning streak to start the season. The game also featured two of the three highest scoring teams in the league.
Briere opened the scoring nearly seven minutes into the first period with his 15th of the year. Off the rush, Briere converted a tic-tac-toe passing play with Vanek and Maxim Afinogenov, redirecting Vanek's feed over Atlanta goalie Kari Lehtonen.
Pominville pushed Buffalo's lead to 2-0 with his 18th of the season with 3:15 left in the second period. After Atlanta defenceman Greg de Vries was caught pinching in from the right point, the Sabres broke away on a 3-on-1, with Vitaly Vishnevski the lone defenceman back. Briere found Pominville in the right circle, and the winger took two strides before wristing a shot past Lehtonen.
Atlanta cut the lead to 2-1 when Metropolit scored his seventh at 2:41 of the third. Standing in the low slot, Metropolit one-timed Jim Slater's pass from behind the goal line to beat Miller.
Vanek made it 3-1 with his team-leading 21st of the season with three minutes left in regulation, and capped the scoring with an empty-net goal with 1:47 remaining.
Lehtonen, making his sixth straight start, finished with 28 saves. He has allowed 14 goals over those starts.
Notes: The Thrashers are two games into a stretch where they play eight of nine on the road. ... Briere snapped his nine-game goal-scoring drought, the longest since going nine games without a goal in the 2003-04 season. ... Pominville has scored in four of his last five games. ... Atlanta also had a five-game winning streak from Nov. 25-Dec. 5. ... Atlanta dropped to 6-3 against Northeast Division teams, while Buffalo is 10-2-1 against the Southeast Division. ... Buffalo D Jaroslav Spacek left the game with 12 minutes left in the third and did not return after blocking Slater's wrist shot. He was favouring his left leg while skating off.