The Canadian had split the first two sets on Friday and was 6-5 ahead when play was suspended because of fading light.
When play resumed on a stifling Court 12, the 13th seed quickly polished off the third set with a break of serve and dominated the fourth to claim a 7-6(5) 4-6 7-5 6-2 victory.
It was fourth time in five years that Raonic had reached the fourth round at Wimbledon.
"I came out with a very different mindset," Raonic told reporters. "I was extremely negative yesterday and just needed to come out with a very different state of mind and different approach today to have a better chance.
"I was extremely passive yesterday."
Raonic, who was runner-up to Andy Murray in 2016, will face American Mackenzie McDonald in the last 16 on Monday.
"He's obviously had good wins through these last three matches here," Raonic said. "It's going to be tough.
"I'll have to stay aggressive and try to dictate more to the rhythm of today rather than yesterday."
(Reporting by Martyn Herman; editing by Clare Lovell)
