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.
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