World champion Luke Humphries beat Mervyn King 10-4 and will face Masters winner Stephen Bunting, who won a final-leg decider against Peter Wright.
Warrington-based Littler meets Australian Damon Heta in the quarter-finals, which will be followed by the semi-finals and final on Sunday.
“It would be unbelievable [to win the title], I have not even thought about it, I will just take it game by game,” said Littler.
He recovered from 5-3 down to overcome German Martin Schindler 10-8 in the last 32 of the event, which is often described as the ‘FA Cup of darts’.
“I think if everyone didn’t know, they are going to know now that I am not a morning person,” said Littler.
“I did struggle this morning but I managed to get over the line against Martin.
“After that game, I chilled out, had some food, and I think played better in the evening, every player thinks they play better in the evening.
“I chilled myself out, went on my phone, went out for some food. This morning I didn’t have breakfast and I was feeling sick because there was nothing in my stomach and my adrenaline was going.”
Smith was beaten 10-9 in the fifth round by Luke Woodhouse, while Anderson went out 10-5 at the next stage to Martin Lukeman.
Littler began the year by becoming the youngest World Championship finalist, before falling to defeat against Luke Humphries.
The teenager took his first PDC senior title by winning the Bahrain Masters and is second in the Premier League behind Dutchman Van Gerwen.
UK Open quarter-finals (13:00 GMT, Sunday)
Stephen Bunting v Luke Humphries
Ricky Evans v Rob Cross
Damon Heta v Luke Littler
Martin Lukeman v Dimitri van den Bergh
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