Henrik Tallinder, Brian Campbell and Jason Pominville also scored for the Sabres (3-0-0), who won their third straight - and first in regulation, after opening the season with two shootout victories.
Jason Spezza scored twice in the third period for the Senators, while Dean McAmmond had the other Ottawa goal as the Senators (1-2-0) lost their second straight at home after opening the season with a 4-1 win in Toronto. They fell 6-0 to the Leafs in their home opener Thursday.
Sabres' backup Martin Biron made 34 saves in his first start of the season, and was especially strong in the second period allowing just one goal as the Sabres were outshot 18-5. The Senators enjoyed a hefty 37-24 advantage in shots before a sellout crowd of 19,202 at Scotiabank Place.
Ahead 2-1 heading into the final period, Drury gave the Sabres a 3-1 cushion when he elected to shoot on a three-on-one break. His shot from the top of the faceoff circle beat Senators netminder Martin Gerber to the far side three minutes into the period.
Spezza pulled the Senators to within a goal when he tipped a Dany Heatley shot past Biron from the slot with less than five minutes to go in the game.
A little more than a minute later, Pominville gave the Sabres their two-goal lead back, but Spezza replied just 10 seconds later, cutting the Sabres' lead to 4-3.
Senators' fans finally had something to cheer about at 11:37 of the second period, when McAmmond rifled a shot into the top corner past Biron for the Sens' first goal on home ice this season.
The Sabres scored on their first shot of the game just 33 seconds in when Ottawa forward Patrick Eaves slid into his own goal, taking Gerber with him. Tallinder gathered a pass from Paul Gaustad and fired into the open net for his first of the season.
The Sabres used the final minute of the first period to collect their first power play goal of the season on their 18th attempt. Campbell extended the lead after converting a pass from Daniel Briere at 19:06. It was Buffalo's first power-play goal of the season in 18 attempts.
Notes: The Senators returned defenceman Tomas Malec to their American Hockey League affiliate in Binghamton. Malec was an emergency call up to replace injured defenceman Tom Preissing for one game. Preissing was back in the lineup SaturdayaThe Senators are off until Thursday when they host the Calgary Flames. The Sabres next play Friday in Detroit.