The five-time world champion needed to win just one frame to book his place in the last eight where he will face Stuart Bingham, although Stevens, who was suffering from a neck injury, won the first frame of the final session before O’Sullivan powered through to the quarter-final.
Trailing 12-4 from Sunday, Stevens cut the gap to seven frames with a 63 break before his 39-year-old opponent ended the contest in the next with a run of 77.
Following the relatively simple conclusion to the match, O’Sullivan revealed he has a much calmer approach in his bid to win a sixth world title.
“Matthew had a really bad neck and I know what it’s like to play with a bad neck.
“He couldn’t even get down on the shots so it was a bit difficult to watch your opponent suffering like that,” O’Sullivan said.
“It was hard for Matt there so it was hard for me to get motivated. I know I only needed one frame so there was no adrenaline there.”
World number six Judd Trump powered into the Betfred World Championship quarter-finals by completing a 13-8 win over Marco Fu with a brilliant century.
Trump, the 2011 runner-up, rattled off a complete clearance of 133 to end the resistance of Fu and book a date with Ding Junhui in the last eight at the Crucible Theatre.
World number eight Shaun Murphy, the 2005 champion, reached the quarter-finals for the eighth time by finishing off Joe Perry 13-5, albeit in scrappy fashion.