Henrik Lundqvist made 22 saves for New York.
The 19-year-old Duclair opened the scoring against goalie Steve Mason with his second of the preseason at 5:31 of the first period before Haggerty scored 2 minutes later.
The 21-year-old Haggerty, signed as an undrafted free agent, scored again at 6:48 of the second. Fast scored to make it 3-0 in the first and tallied again late in the third. Chris Mueller also scored for the Rangers.
The teams play again Tuesday in Philadelphia.