The Devils deadlocked the opening-round series at 2-2 with the critical fifth game scheduled for Saturday on Florida's home ice.
Brodeur was protecting a 1-0 lead leading into the third period but the Devils scored twice in the first 3:35 of the stanza to take control.
Brodeur ran his career playoff record to 101-83. It was his first post-season shutout in three years and only his fourth since he had an astonishing seven of them during the Devils' run to the Stanley Cup title in 2003.
The lone goal in the opening 40 minutes came from Zach Parise on the power play 6:08 into the middle period.
Florida's Scott Clemmensen, who previously was Brodeur's backup in New Jersey, made his first career post-season start and gave up all four goals on 27 shots.
Brodeur has been in the NHL for 19 seasons and has appeared in the playoffs in 17 of them.