Two-time runner-up Carter fought back to take the final two frames yesterday morning to trail 9-7 heading into the evening session.
But he could not keep up the momentum when play resumed and Selby held on, setting up a clash with Alan McManus or Ken Doherty for a place in the semi-finals.
An opening 59 gave Selby the first of three successive frames to open the morning session.
A break of 65 saw Carter pull a frame back but Selby took the next two to extend his advantage.
Carter fired in breaks of 51 and 73 to keep in touching distance, before Selby took control after the interval and clinch his quarter-final spot.
Barry Hawkins and Ricky Walden resume this afternoon with the repeat of last year’s semi-final once again providing drama.
Hawkins stormed out to a 3-0 lead but was pegged back by Walden who drew level at 4-4 at the close of the first session.
And it was Walden, who lost 17-14 to Hawkins 12 months ago, that stepped up the pace in the evening to ensure he heads into the deciding session 9-7 ahead.
Today, sees Judd Trump open up his second-round match against Welshman Ryan Day.
Trump scraped through his opening match, beating qualifier Tom Ford 10-8, and will need to up his game if he wants to reach the last eight,
After beating Ford, Trump said: “It doesn’t matter how you play. If you become world champion, then you become world champion and that is what you need to remember.
“The thing for me is not to get too disheartened.”