Menzies averaged 108.41 and hit six 180s in a high-quality 6-4 success against Cross, one of his principal rivals in the race to Blackpool. The Scot also produced a 170 checkout as he booked a second-round meeting with Stephen Bunting.
“I’ll be honest, I felt really good in that game,” Menzies said afterwards.
“Rob is coming back and he pushed me, but that’s the best game I’ve played in a long time, and I needed that win.”
Van den Bergh also made a successful return after a 420-day absence from the European Tour circuit. The Belgian recovered from 2-0 down to win six consecutive legs and defeat Alan Soutar 6-2, setting up a meeting with Gian van Veen.
The former World Matchplay champion said recent improvements were the result of work away from the stage.
“I am working so hard behind the scenes,” Van den Bergh said.
“I am doing my very best, and you’re seeing glimpses of what I can do again.
“There are parts of my game where I’m performing and showing what I can do, but I can do so much more, and I want so much more.”
Elsewhere, Justin Hood continued his impressive recent form with a 6-4 win over the returning Max Hopp, while Sebastian Bialecki came from 3-1 down to beat James Hurrell and strengthen his own bid for World Matchplay qualification.
Ryan Joyce produced one of the moments of the day with a 150 finish featuring three bullseyes in a comeback victory over Christian Kist. Kevin Doets advanced despite Lukas Wenig producing finishes of 160 and 170, while Jimmy van Schie celebrated his European Tour debut with a 6-0 whitewashing of Ian White.
Dirk van Duijvenbode, Joe Cullen, Niko Springer, Krzysztof Ratajski, Andrew Gilding, William O’Connor, Karel Sedlacek and Ricky Evans were also among the first-round winners.
The tournament continues on Saturday, when Van Veen, James Wade, Nathan Aspinall and Ross Smith enter the competition in the second round.
Results
Round one - afternoon
Ricky Evans 6-1 Teemu Harju
Karel Sedlacek 6-5 Jason Riedtke
Ryan Joyce 6-3 Christian Kist
Jimmy van Schie 6-0 Ian White
Krzysztof Ratajski 6-3 Daniel Klose
Dimitri Van den Bergh 6-2 Alan Soutar
Justin Hood 6-4 Max Hopp
Andrew Gilding 6-4 Jeffrey de Zwaan
Round one - evening
Niels Zonneveld 6-4 Richard Veenstra
Kevin Doets 6-3 Lukas Wenig
Cameron Menzies 6-4 Rob Cross
Sebastian Bialecki 6-3 James Hurrell
Dirk van Duijvenbode 6-0 Paul Krohne
William O'Connor 6-4 Cristo Reyes
Joe Cullen 6-1 Marcel Hausotter
Niko Springer 6-2 Nandor Major