After Englishman White had levelled the match with a 12-dart leg, Noppert seldom appeared bothered in the remaining two sets, with a 95 average and a 116 check-out.
White started on the board with a 14-dart leg, but he had to fight hard for his 3-2 victory, winning eight of the final 11 legs as the match went down to the wire.
In the opening leg of the second set, three-time world champion Van Gerwen came agonisingly close to being the first nine-darter to finish on a 170 in PDC history, but he missed the bull.
Durrant switched to the PDC at the start of last year.
Sherrock began in hot form in the first-round tie, but four missed match darts across two legs cost her dearly as Smith took five straight legs, including a 109 checkout to take the thrilling decider.
The Dutchman’s reign in the Premier League is over after defeat on Saturday night
Van Gerwen had won only two of his previous seven matches on night 15.
Gary Anderson and Peter Wright inched towards a play-off spot.
More drama at Milton Keynes.
The Middlesbrough thrower leads by four points after only one defeat in 12 games.