The Bruins, who began the night having allowed an NHL-low 10 goals for the entire season, won their third in a row.
Lucic put a wrist shot past Ryan Miller for the only goal of the first period and he scored again 40 seconds into the middle stanza.
Boston had only a 3-2 lead heading into the third period, but Krug tallied twice in a span of less than five minutes to break things open.
Buffalo has lost three straight since coming up with its lone win of the season. The Sabres have a 1-9-1 record, their only victory having come in a shootout.
Backup goaltender Chad Johnson had to make just 14 saves to get the win. He is 3-0-1 for the year. Miller surrendered all five goals on 34 shots.