Nicholson saw off German youngster Max Hopp, while van Gerwen defeated Belgiums Kurt van de Rijck.
The world number two set up a tasty last 16 encounter against Mervyn King after seeing off his Belgian opponent.
“It wasn’t my best performance but I’m happy I won,” said van Gerwen, the reigning Premier League champion.
“It was hard to find my game but I’ll make sure it is there for the next one.
“Winning is the most important thing and I’m through so I am looking forward to tomorrow.”
van Gerwen won the first leg on double one before pegging double four for a break of throw.
He scored his first maximum in leg three, which he won by bedding double top.
But his second maximum couldn’t stop van de Rijck from pulling a leg back.
van Gerwen pinned double 16 to restore his three leg advantage and his third 180 helped him move 5-1 in front.
And the Dutchman finished the job by hitting double four.
Nicholson had to fight back from 3-1 down to defeat Hopp and silence the vociferous home crowd.
Nicholson pegged double 16 to win the opening leg but Hopp took the next three in a row.
‘The Asset’ stopped the rot by pinning double seven and he grabbed a crucial break of throw by taking out 56, restoring parity at three legs apiece.
Hopp broke straight back but Nicholson responded in kind when he neatly took out 65.
And the Australian pegged double top to edge ahead and move withing a leg of victory, and he found the same bed to seal the win.
Nicholson faces Andy Hamilton on Saturday afternoon.