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.