Former champion Higgins saw off Michael Holt 6-3, while Maguire showed his very best form in a 6-2 win over Fergal O'Brien.
Maguire produced three consecutive centuries as he destroyed O'Brien 6-2 to make the second round of the UK Championship.
The Scot was matched shot-for-shot early on by his opponent as he struggled to get going early on and slipped 2-1 behind, and the duo went in for the interval all-square at 2-2.
But Maguire then turned on the style, produced breaks of 103, 100 and 131 - the latter including a failed double on the black.
He then wrapped up the match in almost equally brilliant style with a 70 that only came to an end when, brimming over with confidence, he attempted an audacious shot to split two reds that succeeded but left him too much to do with a fine cut back.
There was no way back for O'Brien, however, and Maguire progresses to a second-round match against either Stuart Bingham or Jack Lisowski.
Higgins took the opening frame of his match with Holt, but soon found himself level courtesy of Holt’s 67 break.
A 113 from the four-time former world champion put him back in the lead until Holt squared the contest again, before doing so a third time for 3-3 with a strong comeback following a Higgins run of 50.
Favourite Higgins would finally take control from there, winning three consecutive frames to make the last 16.
Ryan Day emerged from a gritty battle with Ding Junhui to make it into the second of the UK Championship with a 6-4 victory.
A series of tense and lengthy frames between the two saw endless safety exchanges and attempts at snookers as the match crept slowly to 4-4.
Day then got his nose in front after emerging from a lengthy safety battle in the ninth frame, with a series of snookers, flukes and misses finally going the Welshman's way when Ding missed the final red after seemingly having the frame in his grasp.
Twice champion Ding was then dumped out of the tournament as Day seized upon a half-chance at the start of the 10th frame, sinking three very tricky pots to open the table up and give himself an opportunity to clinch the match.
The 32-year-old grabbed that chance with both hands, racking up a brilliant 85 that only ended when he went in-off while chasing a century to finish in style.
Barry Hawkins resisted a Llang Wenbo fightback to win 6-4.
Hawkins got the tournament started in style with a 101 century break before hitting two half-tons as he created a 3-1 lead heading into the mid-session interval.
Wenbo would stage a spirited fightback and win three on the bounce to lead 4-3, scoring a marvellous 107 clearance in the third.
But Hawkins stopped the rot to level the match before creating his own three-frame spell to advance.