The Glaswegian sealed his last eight spot with a 6-4 win at the Barbican Centre but admitted he got lucky.
Maguire said: “I was lucky to get over the line. I was 5-1 up but John has often come back and beaten me.”
Frame one could have gone either way as Higgins, needing a snooker, forced an unfortunate in-off from his opponent. However, he carelessly returned the compliment and Maguire took the frame.
He doubled his lead with the highest break of the tournament so far, a 144 sparked by a superb long red, then calmly cleared the colours to prevent Higgins pinching frame three.
Higgins finally got on the board in the fourth as a plant set up a break of 60 and Maguire failed to get the two snookers he required.
Breaks of 57 and 66 after the interval helped Maguire move 5-1 up but Higgins salvaged some pride with a 101 in frame seven and cleared with 54 to cut the gap to two frames.
The comeback continued apace with a 95 clearance to leave Higgins just 5-4 behind but he overcut a black in the next and Maguire made a match-winning 70.
Fellow Scot and former world champion Graeme Dott also crashed out of the tournament after losing to Australian Neil Robertson.
Robertson took the first and, after Dott levelled via a re-spotted black, the Australian regained the initiative with a break of 71 in frame three and was gifted a topsy-turvy fourth.
Dott missed a frame-ball red into the middle pocket after a break of 56 and though Robertson’s first chance slipped away with poor positional shots to yellow and green, he eventually got over the line to take a 3-1 interval lead.
Dott battled his way over the line in frame five but Robertson took the next and moved to the brink of victory by sneaking frame seven, theatrically patting his heart after the final black wobbled in the jaws before dropping.
Dott stayed in the match after taking frame eight on the black and got in first with 60 in the next, but he missed a difficult long red and Robertson produced a tremendous clearance of 68 to progress to the last eight.
Ding Junhui saw off the 2003 champion Matthew Stevens in another 6-5 thriller.
Ding led 2-1 before Stevens levelled with a 92 – but the Chinese star produced a 133 to regain the initiative.
The breaks kept on coming, Ding with runs of 76 and 65 while Stevens compiled 65, 67 and 72 as the match reached 5-5.
But Stevens broke down on 24 in the decider, allowing Ding to take the match with a 63 clearance.