Littler won a high-quality contest 16-12 in Wolverhampton, where the scoring pendulum swung back and forth between both players.
An intriguing match-up on paper started with a bang as Rock recorded back-to-back 12-dart legs to seize a 3-2 lead.
They both kept within touching distance of each other, as Littler ensured the score remained level after 10 legs.
Rock, though, crafted a 9-6 advantage against a more irritated Littler with 'The Nuke' becoming more wayward.
However, that didn't last long as Littler clawed it back and produced a bull finish to edge 10-9 in front.
An 11-dart leg from Rock chopped Littler's lead down to 13-11, until another bull finish put him on course to close out the match.
"Josh averaged 89 two days ago, and he was never going to do that tonight," Littler said.
"We always bring the best out of each other. Another game and another win, and I'm still unbeaten here."
Facing Littler on Sunday will be Danny Noppert, who fended off Lukas Wenig 16-6 in the evening's other quarter-final.
The pair had already faced each other in the group stage, with Noppert also claiming victory there and showing more of his credentials again.
The turning point came in the 11th leg with Noppert leading 6-4 as a couple of missed checkouts from Wenig gave him a break and reprieve.
From there, Noppert notched another four straight legs, and as the Dutchman seemed to be racing away with the match, Wenig reeled in a classy 170 from nowhere.
That proved to be a consolation for the German, and despite finding his scoring touch late on, the deficit proved to be too large as Noppert closed out the win.