Maguire, a former winner of the tournament himself in 2004, began their encounter impressively with a break of 118.
However, the Australian rallied and rattled off the next six frames to secure his passage to the next round in an imperious performance that included three century breaks.
Robertson, one of only 10 players to have completed the triple crown of the World Championship, UK Championship and Masters, claimed the champions of champions trophy last month and looks in ominous form.
Neil Robertson wins second UK title boosted by stunning 147 break
"That was the best I have played all season, without a doubt. I played great but I knew I had to," said Robertson, via BBC Sport.
"I have to maintain my focus and keep my foot down.
"He looked in really good nick in that first frame and didn't really have a chance up until 3-1 when he was unfortunate to go in off the yellow.
That was the only obvious mistake he made - even though it was very unlucky.
Robertson will face John Higgins in Saturday's quarter-final sneaking past Jamie Burnett 6-4, despite a spirited comeback by the Scot.
The three-time UK champion opened a 3-0 lead and appeared to be on course for a comfortable victory, but Burnett won four of the next five frames to close to 4-4.
John Higgins beat Mark Selby 9-4 to reach the final of the International Championship, where he will face David Gilbert
Image credit: Imago
But Burnett missed a number of chances, including a key miss that could have taken him 5-4 up. That let Higgins in to make a classy break of 102 to go 5-4 up, before closing out the match.
"Jamie came back very strongly and I was fearing the worst for a little while, but I managed to get over the finish line," Higgins told Eurosport shortly after securing victory.
"I'll probably go into the match with Robertson as the underdog and that suits me just fine. These are the kinds of games you look forward to and it will be a great occasion."
Elsewhere, Matthew Selt overcame Luca Brecel 6-4 to also progress to the next round - Selt was 3-1 behind, but won five of the last six frames to secure the win.
Martin Gould is also through after a 6-3 win over Northern Ireland's Joe Swail.
Latest results - Thursday
Neil Robertson 6-1 Stephen Maguire
Matthew Selt 6-4 Luca Brecel
John Higgins 6-4 Jamie Burnett
Martin Gould 6-3 Joe Swail
Robertson whitewashes Selby to set up final meeting with Liang Wenbo
Robertson weathers late Higgins charge