The top-seeded Briton, playing his first event since winning the US Open, looked set for a straightforward victory after taking the first set but faced a battle after Wawrinka levelled the match before eventually winning 6-2, 3-6, 6-2.
The world number three converted four of his 11 break points and won 80 percent of his first serve points to clinch the win in just over two hours, sealing his 50th victory of the year and his 10th straight win.
In the semi-finals on Saturday, Murray, who also won the Olympic title this year, will play sixth seed Milos Raonic of Canada, who beat third seed Janko Tipsarevic of Serbia 6-7 (5/7), 6-2, 7-6 (9/7).
"It was tough. The first set, I started the match well. Stanislas came back into the match in the beginning of the second set," said Murray, 25.
"After that, there were a lot of long games, long rallies. He won at the end of the second set and then I won a couple of long games in the third set, but it was very, very tough with a lot of close games," he added.
Murray got off to an ideal start, breaking in the opening game of the match and repeating the feat later in the set but a single break in the second set was enough for the Swiss seventh seed as he levelled the match.
In the decider, two further breaks for Murray were enough for him to seal the match and a place in the last four.
Results from the Japan Open tennis tournament on Friday (x denotes seeds):
Quarter-finals
Milos Raonic (CAN x6) bt Janko Tipsarevic (SRB x3) 6-7 (5/7), 6-2, 7-6 (9/7)
Andy Murray (GBR x1) bt Stanislas Wawrinka (SUI x7) 6-2, 3-6, 6-2
Marcos Baghdatis (CYP) bt Dmitry Tursunov (RUS) 6-2, 6-4
Kei Nishikori (JPN x8) bt Tomas Berdych (CZE x2) 7-5, 6-4