The Bruins responded with Krug scoring on the ensuing power play.
"We were starting to come around," said Sabres goalie Ryan Miller, who made 29 saves. "We got some life off those goals in the second period. For the most part we cleaned some stuff up. Our transition to defense cost us two but other than that we're in a hockey game."
Chad Johnson made 14 saves for Boston to earn the win.
Boston opened the scoring when Jarome Iginla's wrist shot deflected off Lucic and through Miller's legs.
The Bruins doubled their lead 40 seconds into the second on Lucic's team-leading fifth goal. Iginla fired a pass from the right boards to Lucic and he tapped the puck in before crashing into the boards behind Miller.
Buffalo's first goal came from its struggling power play, which improved to 4 for 38 when Cody Hodgson scored 8:21 into the second period. The Sabres only managed two shots in the third period and were outshot 34-16 overall.
"They've got a strong team from their 'D' all the way up to their forwards and we didn't match them," Sabres co-captain Steve Ott said.
Zadorov's first NHL goal, in just his second NHL game, brought the Sabres within one with 4:50 to play in the second period. Zadorov moved on his backhand around Bruins center before beating Johnson to the left side.
"It feels good for my first NHL goal, first pro goal of my life," Zadorov said. "I'm really happy now."
Zadorov is the second-youngest player to score a goal for the Sabres, at 18 years, 190 days. Pierre Turgeon was 18 years, 54 days when he scored for Buffalo in 1987.
NOTES: First-round pick Rasmus Ristolainen was among Buffalo's scratches, as was Patrick Kaleta who served the sixth game of his 10-game suspension. ... Boston returns home for two games in three nights, beginning with San Jose on Thursday. ... Hodgson has been the Sabres most productive player with a point in seven of his past nine games (three goals, five assists).