Moulson scored 7 minutes apart in the first period to stake the Islanders to a 2-0 lead and added an empty-net marker late in the game for his second career hat trick.
Montoya, who became the first netminder to record a shutout in his Islanders debut Saturday, followed that up with another impressive effort Monday, turning aside 20-of-21 shots to earn a second victory.
The Panthers, meanwhile, lost for the fifth time in seven games.
Tomas Vokoun allowed four goals on 36 shots and Mike Santorelli scored for the Panthers.
Swim Week Miami Beach 2014 [PHOTOS]