"(We wanted) just to attack the stumps as much as possible and, obviously, with Curtis' four-wicket over he did exactly that," skipper Andy Balbirnie said after the win.
"We've had a slow but good build-up, I think we're peaking at the right time."
Campher became only the third bowler in T20 International history to claim four wickets in four balls after Afghanistan's Rashid Khan and Lasith Malinga of Sri Lanka in 2019.
Campher sent back Colin Ackermann (11), Ryan ten Doeschate (0) and Scott Edwards (0) for a hat-trick and then bowled Roelof van der Merwe (0) in a sensational over.
The Johannesburg-born Campher is also just the second player with a hat-trick in the men's T20 World Cup after Australia fast bowler Brett Lee, who achieved the feat against Bangladesh in the inaugural edition in 2007.
Campher, 22, had a T20 best of 3-19 from his previous four matches since making his debut in August against Zimbabwe in Dublin.
He switched ends in the match on Monday and got instant success after Ireland reviewed a caught behind for Ackermann with the ultra edge technology showing a spike when the ball passed the batsman's gloves.
Technology helped Campher once again on the hat-trick ball when Edwards was given not out for an lbw call by the on-field official but replays suggested the ball would have hit the leg stump.
Earlier this season, Campher underwent ankle surgery. "I didn't feel the best, coming back from injury," he said. "First over didn't go as planned but Bal (Balbirnie) kept faith with me."
Skipper Pieter Seelaar scored 21 to take Netherlands past the 100-run mark before quick bowler Mark Adair ran through the tail to return impressive figures of 3-9 -- Ireland's most economical bowling ever in T20 World Cup.
Sri Lanka, the 2014 champions, face Namibia later Monday in the second fixture in Group A.