The world champion edged Aspinall 10-9 in the last 16 at Amsterdam's AFAS Live, taking the final two legs to keep alive his bid to become the first player to win all 10 major televised titles in a single calendar year. He has claimed the opening five.
The result was overshadowed by the reception Littler got from the home crowd. Referee Charlie Corstorphine had to step in on Saturday night, a repeat of the hostility "The Nuke" faced during Friday's victory over Dutch favourite Danny Noppert.
Littler has drawn this line before, staying away from European Tour events in Germany over his treatment there, and told reporters he was "100 per cent" ready to do the same across the border.
'There's no point'
"If the Dutch stay like this, then I'm not going to do any Euro tours over there," he said. "There's just no point in me travelling, wasting my time while I'm getting booed. I just want to play my darts, obviously sign autographs.
"The past two nights, I've done nothing; I've just walked off stage without thanking anybody. There's no point thanking everyone when they are booing me."
On Germany, he added: "I haven't been for a long time, we will have to see in Dortmund whether it changes or stays the same."
Littler faces Jonny Clayton in the quarter-finals on Sunday after the Welshman recovered to beat Motomu Sakai 10-8.
Elsewhere, Gerwyn Price saw off Jim Long 10-5, and James Wade beat Wessel Nijman 10-7 to set up a meeting of former champions, while Josh Rock defeated Ryan Searle 10-7 to set up a clash against Ross Smith, a 10-5 winner over Daryl Gurney.
Humphries bows out
The afternoon session delivered the biggest shock as world number two Luke Humphries went out 10-9 to Dirk van Duijvenbode.
Roared on by his home support, the Dutchman was joined on stage afterwards by his young son Levi.
"Having my kid here is the best thing in my life," Van Duijvenbode said.
"I won this game because he was here. When you are playing against the world number two you are always nervous. When I looked up at him he made me so happy every time. It made me so relaxed. In the end that is the reason I won it."
Van Duijvenbode meets Gian van Veen, a 10-7 winner over Karel Sedlacek, in an all-Dutch quarter-final.
Finals Day concludes on Sunday, with the quarter-finals in the afternoon before the semi-finals and final from 18:00 BST. The winner in Amsterdam takes home £100,000.