Taylor Pyatt's deflected goal put the Rangers ahead in the second period, but Paille assisted Johnny Boychuk at the start of the third then scored himself with 3:31 remaining to put the Bruins 3-0 up in their semi-final series.
The Bruins will try to finish the Rangers off at at Madison Square Garden on Thursday.
The San Jose Sharks evened up their series with the Los Angeles Kings as they held on for a 2-1 win in game four.
Brent Burns put San Jose ahead in the first and Logan Couture doubled the lead in the second, before Mike Richards pulled one back midway through the third.
The teams face off in Los Angeles on Thursday with the series finely balanced at 2-2.