Boston won its third in a row and the defending Stanley Cup champions became the first team in the Eastern Conference this season with 20 victories.
The Bruins were protecting a 2-1 lead heading into the final period and Patrice Bergeron increased the advantage 4:54 into the stanza. Paille tallied less than a minute later and added an unassisted goal with 1:04 remaining in the period.
Tim Thomas gave up two goals on 46 shots while improving his record to 14-5.
Craig Anderson allowed all five goals and made 24 saves. Ottawa had been trying for its first two-game winning streak since late November.