The world champion was made to work hard for the win by Van der Voort, who showed he is back to his best in yesterday’s 6-4 triumph over Steve Lennon, which saw the Dutchman produce a 103.4 average.
Cross, who is gearing up to play in the Unibet Premier League Play-Offs at The O2 on May 17, threw eight perfect darts in the seventh leg of their titanic clash as the wait for a nine-dart finish on the European Tour goes on.
Van der Voort battled from 5-2 down to level the game at 5-5 to set up a tense deciding leg, but Cross held his nerve to fire in a match-winning 12-dart leg.
Cross will now face James Wade in round three as the final day of action takes place at the Glaspalast in Sindelfingen on Sunday.
Wade, who is enjoying a return to form in 2018, booked his place in the third round with a comfortable 6-2 win over John Henderson.
Peter Wright was the stand-out performer on day two of the fifth European Tour event of the year as he threw a stunning 110.29 average en route to a 6-2 victory over Kirk Shepherd.
Second-seed Wright produced four maximums and hit six doubles from ten attempts and will now meet Danny Noppert in round three.
Paul Nicholson reached the last 16 of a PDC ranking event for the first time in over a year thanks to his 6-4 win over Mervyn King.
Nicholson, who played in a final on the Glaspalast stage in 2013 against Wes Newton, showed his battling qualities to record his biggest win over the year.
The former Players Championship Finals winner will look to continue his impressive run in Sindelfingen on Sunday afternoon as he comes up against Jamie Lewis.
Lewis fought hard to record an impressive 6-4 win over Premier League star Daryl Gurney, producing a key break of throw in the penultimate leg of the match to go 5-4 up before sealing his passage into round three.
Ian White opened the afternoon session with a comfortable 6-1 win over Latvia’s Madars Razma and he will now face Dave Chisnall in round three.
Chisnall had to fight back from 4-1 down to eventually grind out a 6-5 win over Matt Padgett, who was playing in his first European Tour event in over four years.
Jermaine Wattimena weathered an early storm as he came back from 3-0 down in an all-Dutch affair with Jelle Klaasen, and he will now meet Premier League Play-Offs star Michael Smith in round three.
World number one Michael Van Gerwen produced a business-like display as he eased past Alan Tabern 6-2, and the Dutchman will now face Darren Webster tomorrow afternoon.
Webster hit a stunning 136 checkout in his 6-3 win over Germany’s Robert Marijanović to end the last hope of a German winner this weekend.
Earlier in the day Joe Cullen silenced the home crowd in a thrilling 6-5 win over Martin Schindler, and will now come up against Kyle Anderon after his win over Kim Huybrechts.
Simon Whitlock produced the only whitewash of the day with his 6-0 win over Jan Dekker, and the Australian will now face Mensur Suljovic in the third round, after his narrow 6-5 triumph over Jamie Caven.
The European Darts Grand Prix will conclude on Sunday, with the afternoon session's third round followed in the evening session by the decisive quarter-finals, semi-finals and final.
The European Darts Grand Prix will be broadcast throughout the weekend for PDCTV-HD Subscribers, and through a series of bookmakers' websites worldwide.
Saturday Results
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Afternoon Session
Ian White 6-1 Madars Razma
Dave Chisnall 6-5 Matt Padgett
Jelle Klaasen 3-6 Jermaine Wattimena
Joe Cullen 6-5 Martin Schindler
Gerwyn Price 5-6 Danny Noppert
Michael Smith 6-5 Arron Monk
Kim Huybrechts 4-6 Kyle Anderson
Simon Whitlock 6-0 Jan Dekker
Evening Session
Daryl Gurney 4-6 Jamie Lewis
Darren Webster 6-3 Robert Marijanovic
Mervyn King 4-6 Paul Nicholson
Mensur Suljovic 6-5 Jamie Caven
Michael van Gerwen 6-2 Alan Tabern
Peter Wright 6-2 Kirk Shepherd
John Henderson 4-6 James Wade
Rob Cross 6-5 Vincent Van der Voort
Click here for Sunday schedule
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