The teenager looked briefly undone as Welsh star Price stormed into a 2-0 lead, but Littler produced a composed response to reel his opponent back in and snatch victory in a tense deciding set.
Earlier, Danny Noppert defeated Scotland’s Gary Anderson 3-1 to advance to the semi-finals. The Dutchman will face either Luke Humphries or Cameron Menzies tomorrow night.
In the other quarter-final action, Dirk van Duijvenbode eased past Jonny Clayton, defeating the Welshman three sets to nil to set up his meeting with Littler.
Results & fixtures
Danny Noppert 3-1 Gary Anderson
Dirk van Duijvenbode 0-3 Jonny Clayton
Luke Littler 3-2 Gerwyn Price
Luke Humphries v Cameron Menzies