Chris Phillips also scored for Ottawa, winners of five straight road games and six of seven overall. The Senators have won the last two meetings against Boston after losing the first three this season.
It was just the second time Boston has been shutout this season; the other came in a 5-0 loss at Nashville on Dec. 30.
Hannu Toivonen, looking for victories in consecutive starts for the first time this season, stopped 36 shots for Boston.
The Bruins matched their lowest shot total this season.
Heatley's second goal was a shorthanded, empty-netter in the closing seconds.
Ottawa grabbed a 1-0 lead on Phillips' goal 17:16 into the opening period when he collected the rebound of Peter Schaefer's shot at the bottom of the left circle and slipped a shot past Toivonen.
The Senators made it 2-0 on Heatley's power-play goal 15:03 into the second period. Tom Preissing fired a shot from the point that Toivonen stopped, but the puck slipped behind him and Heatley backhanded it into the open net.
Ottawa had an excellent chance for more scoring when it was awarded a five-on-three advantage late in the second period. Boston defenceman Andrew Alberts was given a five-minute major for boarding and Marc Savard was called for unsportsmanlike conduct.
The Senators had another two-man advantage midway into the third, but Toivonen kept them scoreless with a couple of good stops on shots from close.
The Senators kept the Bruins' offence in check for most of the first two periods, owning a 26-12 shot advantage. Boston's first decent scoring chance didn't come until Savard broke in on a partial break two minutes into the second, but Emery handled the shot easily.
Notes: Boston RW Glen Murray's next assist will be the 300th of his career. ... Ottawa D Christoph Schubert was whistled for diving while attempting to draw a penalty late in the second period. ... The teams meet again in Ottawa after the all-star break next Saturday.