Penrith continued to enjoy the better of field position after the break for Kevin Naqaima to cross out wide in the 57th minute, with Moylan again throwing the last pass.
The Tigers finally scored in the 53rd minute when Blake Austin stepped his way over to give the raucous home crowd some hope.
But that was dashed just three minutes later when Jamal Idris strode over out wide and Whare scored his double six minutes later.
Brent Kite toiled away strongly up front all day for the Panthers in his 300th NRL game and five-eighth Jamie Soward led the team well without Wallace.
In contrast the Tigers were largely directionless without their skipper and NSW rake Robbie Farah, with youngsters Mitchell Moses and Matt Lodge making solid NRL debuts.
Panthers duo Elijah Taylor and Adam Docker left the field late for the Panthers with concussion, while Tigers pivot Braith Anasta suffered an arm injury.
Anasta was placed on report for a dangerous throw on Idris, his teammate Bodene Thompson earning the same with a late first half hit on Jamie Soward.