Despite a close start, with Littler holding a narrow 3-2 lead after five legs, the 18-year-old took control of the match.
His impressive display included seven maximum 180s and an average of 107.30, significantly outpacing van Veen's 99.82.
"Myself and Gian have played many times, both our throws suit each other and we just like to get on with it," Littler said to ITV, attributing his success to their familiar playing styles.
"That certainly helped me. I am very happy with my performance. It's another win and I'm back tonight for the final session."
Awaiting Littler in the semi-finals is Welshman Jonny Clayton, who progressed after securing a hard-fought 10-8 victory against former world champion Michael Smith.
Meanwhile, world number one Luke Humphries suffered a shock defeat to James Wade in a thrilling 10-9 encounter.
Cool Hand Luke missed six darts for an opportunity to make it 9-7 before Wade made a late surge to steal a stunning victory.
Northern Ireland's Josh Rock, who defeated Nathan Aspinall 10-7, will take on the victorious Wade.
The UK Open concludes during Sunday's evening session from 19:00 GMT.
The tournament winner picks up a top prize of £110,000.