The three-time champion showcased his class with breaks of 62, 108, and 93, establishing a commanding 4-0 lead at the mid-session interval.
Carter, despite a brief resurgence in the second half, struggled to contain Selby's dominance. The Jester from Essex could only manage a single frame as Selby continued to impress, culminating in a sublime 126 break before sealing his victory with a half-century contribution.
"I played in the Championship League last week and felt I was hitting the ball quite well," Selby told the BBC.
"It is nice to carry it on and bring it into a tournament as big as this.
"You are only human and you can easily come out and collapse with this crowd. There is a lot of pressure out here."
Selby will now face the winner of the match between Mark Allen and Si Jiahui in the quarter-finals.
Earlier in the day, Ding Junhui overcame a spirited fightback from Mark Williams to clinch a 6-5 victory in a dramatic final-frame decider.