Jagr, who left the NHL for three years before returning last season to continue what has been a 19-year career, was acquired by the Bruins this week in a trade with Dallas.
He had scored 14 goals for the Stars in 34 games and quickly made his presence felt by tipping in a shot early in the second period against fellow-veteran Martin Brodeur.
Rask made 40 saves in earning his third shutout of the season and the 14th in his six seasons with the Bruins.
Boston won its third in a row and moved within four points of Pittsburgh for the most in the Eastern Conference.
New Jersey had dropped five straight. Brodeur stopped 25-of-26 shots.