The Ducks were closing in on what would have been their fourth straight victory when Zedeno Chara lifted Boston into a 2-2 tie with 2:50 to play in regulation. Chara's goal came with Anaheim's Patrick Maroon in the penalty box for throwing his stick.
Boston then halted a two-game skid with Iginla's goal, which stood up thanks to three saves in the shootout by Tuukka Rask.
The Bruins' other regulation goal came from Carl Soderberg, his first in the NHL. That came midway through the second period and tied the contest at 1-1.
Devante Smith-Pelly gave Anaheim the lead with the only goal of the first period and Mathieu Perreault put the Ducks in front 2-1 by scoring with 21 seconds to go in the middle stanza.
Rask and Anaheim's Jonas Hiller both stopped 21 shots.