Hours after Lee Chong Wei of Malaysia had been sent packing late on Wednesday, the fifth-seeded Lin suffered a wobble before the gifted Chinese found his rhythm to beat Sasaki 20-22 21-6 21-8 in the last 16.
"It took me time to get into the match but I changed my tactics, stayed calm and I'm really happy to get through," Lin said after his 64-minute win.
Lin had looked comfortable in the opening exchanges but he suffered a mid-game crisis from 13-9 up as Sasaki found himself with three game points.
Lin got himself out of trouble thanks to a superb low retrieval at the net and a smash winner before the world number 20 Sasaki sneaked the opener.
However it was the last meaningful contribution by the Japanese, with Lin shifting through the gears to set up a quarter-final meeting with Denmark's Jan O Jorgensen, the 2015 finalist, who ousted Hong Kong's Ng Ka Long Angus.
"He is one of the best in the world and I will have to play my toughest match yet to beat him," Lin said of Jorgensen.
Lin will head into that encounter unbeaten in 14 matches since November and showing ever-improving form with the Rio Olympics looming in August.
Asked whether he was a different player to 2008, when the 33-year-old won his second Olympic gold, Lin said: "There are more challenges than before. It's about getting the best out of myself and I am clear about the circumstances."
Lin and Jorgensen were the first big names through to the quarter-finals, with defending champion Chen Long of China and Dane Viktor Axelsen also in the top half of the draw.
With Lee's exit, attention has shifted towards Kento Momota, the Superseries Finals champion, who is a potential finalist and the highest seed left in the lower half.
The other threat lies with eighth-seeded Tian Houwei. The Chinese enjoyed a huge celebration after coming through 10-21 21-12 21-19 against Sameer Verma of India in a 67-minute tussle.
Ratchanok Intanon, the 2010 women's singles finalist, looked in fine form as she progressed to the quarter-finals for the fourth time.
Thailand's number one beat Akane Yamaguchi of Japan 21-9 21-13.