Littler averaged 114.47, nearing Phil Taylor’s tournament record of 118.14, in a dominant display against Aspinall.
The world number one won the first four legs in 12, 11, 12 and 11 darts, taking a 4-0 lead with an average above 130. Aspinall hit 10 maximums and fought back to trail 5-4, but Littler regained control to seal his place in the last eight.
"I felt really good from the off tonight," he said. "Nathan is always there. He’s always going to come back at you, so I couldn’t afford a drop-off.
"I looked up a few times, and I think I was on a 121 average and 117 at some point, so I told myself (...) just keep going.
"I’ve had a long time off and past results haven’t gone my way, but hopefully if I do lift the trophy, I can say I've not gone anywhere!"
Littler will face Krzysztof Ratajski in the quarter-finals after the Pole recovered from 4-0 and 8-6 down to beat Kevin Doets. Ratajski hit seven 180s and averaged almost 97 on the way to victory.
Woodhouse followed his nine-dart finish on Thursday by beating defending champion Van Veen 10-6. Ross Smith is now the only former champion remaining in the tournament, and he will face Woodhouse in the quarters.
"Being in the quarter-finals is huge," said Woodhouse, who took out finishes of 114, 117 and 129 against the Dutchman.
"When someone of Gian’s quality is not at it, you’ve got to pounce on them and make sure you don’t let them back into the game.
"I was very steady, and I took my chances, but I have another big game tomorrow."
Smith kept his bid for a second European Championship title on track with a 10-7 win over Damon Heta. The top seed averaged 112 as he raced into a five-leg lead, then overcame problems on the doubles to secure victory.
Martin Schindler delighted the Dortmund crowd by beating Jermaine Wattimena 10-4 to set up a quarter-final against Jonny Clayton. Roared on by more than 7,000 fans, the German number one converted 53% of his attempts at doubles.
Clayton survived a late fight-back from Josh Rock to win 10-8, sealing the match with a 121 checkout on the bullseye after the Antrim native had threatened to recover from 9-6 down.
Gerwyn Price and Stephen Bunting will meet in the quarter-finals after emphatic victories over Cameron Menzies (10-4) and Kim Huybrechts (10-3), respectively.
The tournament concludes at the Westfalenhalle on Sunday, with the remaining eight players competing for the £150,000 first prize. The quarter-finals take place in the afternoon, before the semi-finals and final begin at 19:00 CET.
Results
Round two - afternoon
Gerwyn Price 10-4 Cameron Menzies
Stephen Bunting 10-3 Kim Huybrechts
Ross Smith 10-7 Damon Heta
Luke Woodhouse 10-6 Gian van Veen
Round two - evening
Krzysztof Ratajski 10-8 Kevin Doets
Martin Schindler 10-4 Jermaine Wattimena
Luke Littler 10-5 Nathan Aspinall
Jonny Clayton 10-8 Josh Rock