The 43-year-old from Wishaw will now meet Judd Trump in a repeat of the 2011 final.
Trump was 21 when he lost that showdown to Higgins eight years ago but the experienced Scot acknowledged he will be facing a different challenge.
Four-time winner Higgins said: “Judd is an unbelievable all-round player now, while when I played him in 2011 he was just crash, bang, wallop and normally they were going in.
“I’ll be playing a different Judd Trump. The way he dismantled [Ronnie] O’Sullivan in the Masters has given him the confidence to come here as one of the favourites.”
Higgins staged a remarkable recovery to reach this year’s Crucible showpiece. He hit a 139 total clearance to set up the one-frame shoot-out then capitalised on a missed black by Gilbert to fire what would prove to be a match-winning 55 break and clinch a 17-16 win.
The Scot had started the final session 13-11 down but went on to cap an astonishing career revival having intimated he was ready to retire after losing in the second round of the UK Championships late last year. Higgins, a four-time world champion, said: “I was at a low ebb around Christmas – probably the lowest ebb I’ve ever been in playing the game.
“I can’t really explain to be honest. I apologised to Dave – I told him I brought him down to my level in the first three sessions.
“I was really poor and I think Dave really let me off the hook. I was over the moon to be only 13-11 [on Friday night]. I was feeling good but nothing was happening.”
The Scot’s dissatisfaction had again been plain to see in the second session on Friday which was classed by some snooker experts as one of the worst he has ever played.
Indeed it was Higgins who was more pleased with the overnight scoreline and, despite Gilbert firing a 105 clearance in the opening session of the day, there was a hint of inevitability about the Higgins comeback.
Four frames in a row duly followed as Higgins grabbed the lead at 15-14 for the first time since the fifth frame, suggesting that he had repelled the challenge of the Tamworth player.
But Gilbert levelled with a 78 then went one frame from victory before Higgins drew on his vast reserves of experience, first with his stunning clearance then after a cagey safety battle which saw him over the line.
Tearful Gilbert, who had arrived at the tournament with few expectations but twice blew a five-frame advantage in the match, broke down in tears in the post-match press conference.
Gilbert said: “I’m absolutely gutted to lose. I could have got to a world final but I’ve got nothing to feel sad about. I came here with no expectations and to end up on the one table against a legend like John, it was an honour.”
Trump reached the final by completing a 17-11 victory over Wallsend qualifier Gary Wilson.
Resuming the evening session with a four-frame advantage, Trump wrapped up victory in style with breaks of 97 and 88 to end the colourful run of the former taxi driver and factory worker.
Along the way Trump wrote a new piece of Crucible history as his 114 break in the 20th frame represented the 87th century of the Championship – eclipsing the previous mark set in both 2015 and 2016.