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.
Kevin Poulin made 20 saves for New York.
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