The Islanders got to Devils goalkeeper Martin Brodeur for four goals on just eight shots over the first 20 minutes.
Anders Lee got the Islanders going with a power-play goal just 3:32 into the game. Bailey then made a steal at the top of the circle, skated in alone and fired it past the 41-year-old Brodeur for a 2-0 lead.
Rostislav Olesz got the Devils on the board before Bailey struck again, firing a backhander past Brodeur with 1:55 left in the period. The Islanders scored again when Eric Boulton skated free out of the penalty box and took a perfect pass to push the lead to 4-1 with just 25.6 seconds remaining.
Kevin Poulin made 20 saves for New York.
Marek Zidlicky and Jon Merrill scored for New Jersey in the first part of the second period. Merrill finished with a goal and an assist.