Larne took the lead in their game midway through the first half when Lusty drilled a drive into the corner of the net from the edge of the box after home goalkeeper Jason Craughwell punched away a corner.
The visitors double their lead two minutes after the break as Benji Magee’s pull back from the right-hand side found the net with the help of a deflection from a home defender.
Lusty completed his double in the 50th minute after Mark Randall played a ball into the box which he controlled, before rifling a volley into the corner.
Millar then got his name on the scoresheet soon after being introduced as a substitute, the former Ballymena player getting on the end of Tomas Cosgrove’s pull back from the right and making no mistake with his finish.
After a goal-less first half at Holm Park, Curran out Cliftonville in front early in the second half and then Hale doubles his side’s advantage as he found the bottom corner after good work by Michael Glynn.
Teenager Madden scored the Reds’ third at the end after good work by Jack Berry.