In a repeat of January's World Championship final, Van Veen overcame a late surge from Littler - who fought back from 4-1 down to level the score at 5-5 - to progress to the semi-finals at Manchester's AO Arena.
But the match was marred by some unusual scenes in the dying embers, as Littler and Van Veen exchanged words, gestures and less-than-friendly facial expressions.
After Littler missed a double seven to take out 134, Van Veen also missed inside on double 15 to hand another opportunity to the reigning world champion, who turned to the crowd and beckoned them to cheer his opponent's failed attempt.
Littler - who had received some boos from the Manchester crowd despite being a die-hard Manchester United fan and Warrington native - then exchanged some angry words with Van Veen before himself going inside on double seven, resulting in him gesturing a crying motion towards his opponent.
World number three Van Veen then returned to the oche to sink double six and clinch the victory, before more words and a frosty handshake were exchanged prior to Littler storming off the stage.
'Not a good loser'
"I'm on 90, I miss double 15 on the inside, and then I see him celebrating towards the crowd. I don't think that's normal," Van Veen said afterwards.
"And then he also makes that crying gesture.
"He's a fantastic darts player, but today he showed he's not a good loser. Celebrating a miss from your opponent, that really annoys me.
"That's why I gave him a look. The fact he then misses three darts at a double, that's his problem.
"He was celebrating me missing double 15. That's out of order. I was fuming about that.
"And he missed three darts at double seven. Then he looked at me like I was the problem. He is probably fuming.
"That's my perspective. His perspective is probably different.
"I love Luke to bits. All the attention he has brought to the sport is phenomenal, but today was my day."
After the match, Littler was quick to take to social media, first posting a screenshot of his major trophy wins listed on Wikipedia with a message "thanking" Manchester, followed swiftly by a shared quote from Van Veen and a series of laughing emojis.
'Gian handled it better'
"Van Veen went inside on D15, and Luke was happy about that, so it kind of gave it the Simon Whitlock 'well done'," commentator Wayne Mardle explained on Sky Sports during the live broadcast.
"You shouldn't do that and as he has done that, Gian has turned around thinking 'Why did you do that?'
"I can lip-read, but I won't repeat what Luke said as I don't want to hand in my notice! You have got to say that Gian handled it better."
Van Veen would go on to beat Josh Rock 6-3 in his semi-final.