The 39-year-old Scot, who is only in the eight-man tournament due to Ding Junhui's inability to travel from China, was in unstoppable form, at one point compiling four 100-plus breaks on the spin.
Only Stephen Hendry, who scored seven centuries in his UK Championship final win over Ken Doherty in 1994, has compiled more centuries in a match away from the Crucible.
Maguire said: "I would say that's the best I've ever played – maybe it's because we've had a break and there wasn't a lot of expectation there.
"I really didn't know what was going to happen. Some days you wake up and you can't do anything right, and other days you play like that.
"I don't think anybody could expect to do that again, but you've just got to keep hammering away. If I play half as well as that again I know I will put up a fight."
The pair shared four centuries in the afternoon session, which finished level at 4-4, before Maguire, in his first match since emerging from lockdown, turned on the style.
From 5-4 behind, he hit successive breaks of 104, 135, 127 and 127 again, before wrapping up victory in style with a 59 clearance after Robertson had broken down on 53.
Maguire, who reached the UK Championship final late last year, will face either Judd Trump or his best friend and practice partner John Higgins in the last four.