Carter, a 50/1 pre-tournament selection for this columnist, didn't drop a frame in his opening match against Kurt Maflin and maintained that strong level of form in a high-quality affair against Maguire.
It was Maguire who drew first blood, winning the opening frame thanks to a break of 90, but a run of 81 saw Carter level the scores before the next two frames were shared to leave matters all square at the mid-session interval.
Breaks of 93 and 76 gave Carter the lead for the first time in the match and he looked sure to go three frames clear in frame seven when well-set on 52.
However, Maguire was handed a lifeline and kept himself alive with a nerveless run of 68 before the Scot levelled the scores when taking another tight frame thanks to a break of 52.
Carter wasn't perturbed, however, and set up a third-round clash with Akani Songsermsawad by taking the next two frames with breaks of 75 and 107.
Selby marches on
Defending champion Mark Selby looks to be finding his form just at the right time and saw off Robert Milkins 6-4.
Breaks of 57, 102 and 131 put Selby firmly in control at the mid-session and he extended his lead to 4-1 when taking frame five.
A break of 112 kept Milkins in the hunt, though, and he added frame seven to reduce his arrears to 4-3.
However, a missed red with the rest from Milkins in the following frame allowed Selby to go two clear once again and despite a rally from Milkins in the next, Selby won frame 10 to take the honours 6-4.
Trump and Ding safely through
Judd Trump didn't need to be at his best to beat Michael Holt 6-1.
Holt impressed when beating Luo Honghao in the previous round but he failed to fire against Trump whose top break was only 52 in a forgettable affair.
Meanwhile, Ding Junhui impressed when battling past Zhao Xintong 6-4 and he will play Matthew Stevens in the next round after Welshman overcame Mark King 6-5.
Neil Robertson, Mark Allen and Jack Lisowski are others to have claimed wins on Tuesday.
