Selby had taken a 3-1 lead into the first mid-session interval though both players struggled to find form amidst tricky conditions in the Crucible Theatre.
But with the cue ball replaced and the table brushed, Bingham resumed like a man possessed.
Breaks of 92 and 82 helped the Essex potter turn the tables on the three-time world champion, looking good to go in with a 5-3 lead when in the balls in the eighth and final frame.
But a superb clearance under intense pressure helped Selby stop the rot, with the first to 17 booking their place in the World Championship final.
“Selby struggled, Bingham looked fluent, but when you look back on a World Championship, it’s a session that you got out at 4-4 instead of being beaten 7-1 which is the reason you’re sitting there with the trophy,” said Eurosport pundit and six-time world champion Ronnie O’Sullivan.
“I’ve felt like that a lot of times. It’s those sessions that will win you the trophy.”
Bingham has played more snooker than anyone still standing in Sheffield having been forced to win two qualifying matches just to reach the main event.
But you could never call his place at the Crucible undeserved, opening up his first semi-final since winning the title in 2015 with a composed break of 60.
Both he and Selby have played some wonderful snooker throughout the tournament so far but, with the one-table setup now in operation, free-flowing brilliance wasn’t in store in the opening stages.
Neither were able to make significant breaks early on but Selby – who had trailed for the first time in the entire tournament after the opener – seized the initiative to take each of the next three frames.
His lead was certainly no surprise, with victories of 10-1, 13-7 and 13-3 seeing him concede just 11 frames in the first three matches of the tournament, equalling the Crucible record.
Quarter-final victory over Mark Williams was secured with a session to spare but he was left in his chair for large stages of an excellent second half-session of snooker.
Bingham was not without his good fortune, pulling off a remarkable fluke to set himself up in the fifth frame.
A break of 92 saw him capitalise on the luck, while Selby’s early foul in the sixth helped his opponent pull the game back to 3-3 in the first of four sessions
With plenty of snooker still to play, the match was never going to be won in the opening eight frames in Sheffield.
But momentum was certainly in Bingham’s favour, once again enjoying plenty of table time in the seventh.
A break of 82 – his third over 50 – restored a lead he had relinquished following the opening frame.
Back in the balls once again, it looked nailed-on that Bingham – who beat Anthony McGill in a 13-12 quarter-final thriller – would enjoy an overnight lead heading into two sessions on Friday.
Having 42 on the board while playing well made that look a formality but he broke down when well positioned in the break.
Selby has played excellent snooker throughout the week but even he could be forgiven for being rusty when returning to the table.
The fact that he scored seven points after the resumption compared to Bingham’s 321 spoke volumes for how the session was panning out.
But the Jester from Leicester is not seen as one of the toughest match players for nothing, playing some phenomenal shots while holding his nerve to pinch what could be a vital last frame.
The two resume at the Crucible on Friday morning, with the third session being played on Friday evening before the match concludes on Saturday afternoon.
The winner will face either Kyren Wilson or Shaun Murphy on Sunday and Monday, after the English pair opened their semi-final on Thursday evening.
*Watch the World Snooker Championship live on Eurosport and Eurosport app from April 17- May 3