Littler received a positive reception from the Alexandra Palace crowd, a contrast to the boos he faced in his previous match, and will now face Ryan Searle in the semi-finals.
Gary Anderson also reached the semi-finals for the first time in four years, defeating Justin Hood 5-2, and is aiming to become the oldest PDC world champion.
Anderson is set to play Gian van Veen in the semi-final, after Van Veen delivered a spectacular 5-1 win against Luke Humphries, elevating him to world No 3.
Ryan Searle, Littler's next opponent, has not dropped a set en route to the last eight and secured his semi-final spot with a 5-2 victory over Jonny Clayton.