McManus, a close friend and practice partner of Higgins, claimed his first victory at the Crucible since 2005, roaring into a huge lead before holding off a spirited late surge from the former world number one to advance.
After losing the opening frame, McManus responded with a fine break of 94 before going on to claim the following five frames as he led 6-1.
A break of 80 seemed to have given Higgins some momentum as he went on to reduce the deficit by two, though long-time friend McManus appeared to be on his way to sealing victory as he regained form to lead 8-3.
However, The Wizard of Wishaw produced a stirring fightback – which included a break of 111 – to put pressure on the veteran by winning four of the next five frames.
Higgins's comeback fell short, however, as McManus held his nerve to see out the victory.
"I scraped over the line in the end. When he started coming back, it was no surprise," said McManus. "If John starts relaxing and putting his arm through the white the way he can, then it can be like trying to tame a lion.
"Fortunately I got another couple of chances which I badly needed towards the end. I got a bit ahead of myself and thought 'this is a chance, put it away and get done and dusted' and I made a mess of it and put myself under pressure."
In the day's one other result, Ricky Walden came through a lengthy battle with Kyren Wilson 10-7, a match which included a marathon 17th and final frame which lasted 73 minutes.
That epic fell just short of the longest frame in Crucible history, and the 75-minute mark set by Stephen Maguire and Mark King in 2009 still stands.
Walden next faces either Barry Hawkins or David Gilbert in the last 16.
"I was enjoying myself - it was a very tricky frame to come through and I'm glad I did in the end," said Walden. "I was just waiting for my chance. I just stayed positive and eventually got over the line. We both lost our technique out there a little bit. It was a crazy frame.
"Kyren's a very good player. He's going to be around for many years. I'm just pleased to be in the next round. I knew it was going to be a tough game. You're always looking to play your way into a tournament. I'll be focusing on the next game now and hopefully I can play a little bit better."
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- Ricky Walden