New Jersey became the fourth Eastern Conference team to reach 70 points for the season and Brodeur won for the 645th time in his 19 NHL seasons.
After a scoreless first period, Adam Henrique and Alexei Ponikarovsky scored for the Devils in the opening 11 minutes of the second.
Corey Perry brought the Ducks within one with his 29th goal, coming with 3:52 left in the middle period, and Sheldon Brookbank tied it with just 2:13 left in regulation.
Brookbank has played 253 games in the NHL over six seasons and this was only the second career goal for the Anaheim defenseman. The other one came three years ago.
Brodeur made 36 saves while Hiller stopped 25 shots before giving up two goals in the shootout.