On his way to victory Maguire compiled the tournament's highest break so far - a 142 - and will next meet either Neil Robertson or Joe Perry, who play on Wednesday.
"I wasn't quite sure what the high break was when I was on it," said Maguire. "I knew there had been a 139 and someone said that had been beaten today so I was trying to get as many blacks as I could.
"I felt good after the interval. John struggled all the way through the match but I was struggling over the first four. I should've been 3-1 up maybe even 4-0 with the chances I had.
"If I play Robertson, the world number one, it will be a good match if he manages to turn over Joe Perry but Perry's playing some good snooker at the moment. He won his first pro tournament in Asia and he's in the top 16 and fighting for the Masters as well so he'll be up for every single match.
"I've got a day off now though and I can watch the other boys try their hardest and I'll be totally refreshed for Thursday."
Joining Maguire in the last eight is Barry Hawkins, who saw off Shaun Murphy 6-5 in a late-finishing match at the Barbican.
Hawkins took advantage of a long red from Murphy in a deciding frame and he went on to make a break of 70 which was enough to seal victory.
Graeme Dott or Mark Selby await in the quarter-final.
"I got to about 48 and I just came a bit too far on the black," said Hawkins. "I was going to play a cannon and I talked myself out of it and just concentrated on winning the match because that is the most important thing.
"I didn't do that much wrong to be behind in the early stages and just dug in to come back to 2-2. Shaun could've been 3-1 up I suppose so I was delighted at 2-2.
"Dott is really back in form, he beat me in the PTC in Antwerp and he looked really good again so I think Selby has got a really tough game there."
Last 16 results:
Maguire 6-3 Higgins
Hawkins 6-5 Murphy
Remaining last 16 matches:
Selby v Dott
Trump v Allen
Walden v Ding
Robertson v Perry
Morris v Bingham
Milkins v O'Sullivan