Mei, who stunned Ronnie O’Sullivan at the last-16 stage on Thursday, opened a three-frame advantage over Selby courtesy of runs of 108 and 56.
However, the three-time world champion, outlasted world number 70 Mei in a tactical frame four to cut the arrears before the interval and breaks of 69, 70 and 132 put the Jester from Leicester to within a frame of the semi-final.
And Selby, 36, drew on all his experience to seal the win to make it five frames on the bounce and confirm his place in the semi-finals, where he will face Mark Allen.
David Gilbert produced two superb final frames to see off Ricky Walden 5-4 and book his place in the English Open semi-finals.
Gilbert, ranked in 12th, 17 places ahead of his opponent, had started the match at a canter, winning the first two frames thanks to breaks of 85 and 63.
'Well played' - Walden sinks brilliant double
Walden refused to be beaten, however, and came back with aplomb, winning the next three frames, the highlight of which was a break of 125 without reply to level it up in the fourth.
It looked like an upset might be looming when Walden went 4-3 up after winning the seventh frame but two 50-plus breaks allowed Gilbert to stave off an upset.
"It was a good game, I really enjoyed it," he told Eurosport after the match.
Every time Ricky got going, he was taking his chances and it was nice and free-flowing, so I'm sure it was all right to watch. It was definitely a 50-50 game, Ricky's a quality player.
"I'm just enjoying my snooker at the minute. I feel like I've been close to playing well but I've been struggling in matches. We've worked on a couple of things I was doing wrong and I've tried to focus on that more rather than actually playing and it's really helped me this week."
He was the first player to reach the last four in Crawley, and will face Tom Ford in the semi-finals.