Littler, who had recovered from a 7‑2 deficit in the previous round to beat Jermaine Wattimena, entered this tie as a heavy favourite after averaging a huge 109 in that second‑round tie but was taken to the brink by 2023 UK Open winner Gilding in front of a rapturous crowd.
"I think you wanted 15-15!" Littler told Sky Sports after the win.
"That last leg, I just had to stay focused and get over the line. He won a few on the bounce when I was sitting on 15 legs, but I just had to do a professional job in the end.
"I didn't really panic. Andrew started to win a few legs, but that last leg against the darts as well. I just had to get over the line.
"Andrews does what he does. He never goes out of rhythm. It's the same, throw by throw, and try to match him."
The opening legs followed throw, five in a row, before Littler claimed a break with a maximum followed by a two‑dart 90 finish for an 11‑dart break of throw, taking a 5‑3 lead.
Gilding - who won their last meeting at the European Championship in October - answered with heavy scoring but trailed for the remainder of the match, struggling to cut the gap from three, sometimes four legs.
Littler's finishing had looked shaky earlier in the tie but gradually sharpened into form.
However, Gilding - at one point averaging over 113 in the latter stages - landed a decisive 72 bull finish to break at 14-11, before sinking an impressive 160 to make it 14-12. Littler's narrow advantage heading into the closing stages suddenly looked under threat.
Another break would come when the 54-year-old took the tie to 15-14 with a stunning 127 despite an impressive nine darts from The Nuke, who himself had set up 161 for the match.
Yet Littler would not be denied, mopping up an excellent 11-dart leg with back-to-back 180s before taking out 41 for a scintillating finish to ultimately seal the 16-14 victory.
Littler averaged 103.91 to Gilding's 98.45, but the reigning world champion blew his opponent away with an astonishing 18 maximums.
Rock rocks Price to set up Littler semi
Littler will face Northern Ireland's Josh Rock in the semi-finals, who defeated in-form Gerwyn Price 16-11 in the evening's second match.
Fresh off the back of stunning victories over Michael van Gerwen and Ross Smith, and a rematch of the World Cup final in June, when Rock and Daryl Gurney stunned Wales' Price and Jonny Clayton 10–9, Rock again impressed in Blackpool.
Price opened the night with a 13-darter, immediately laying down the gauntlet, but Rock responded in kind, quickly pinning tops for a 13-dart hold.
The 24-year-old Rock then produced a magnificent 120 checkout on tops to nose ahead, setting a tone for a match packed with power scoring and clinical finishing.
The contest's pivotal section arrived as Rock started to stretch clear at 6-4 with a 10-dart leg that left Price shaking his head.
The Iceman, 2022's runner-up, had shown signs of fight with a timely 170 checkout - the tournament's first this year - but as the pressure mounted, so did the missed doubles.
Rock ruthlessly capitalised, hammering in nine maximums by the 24th leg and maintaining an average above 105 at key intervals.
As the winning line loomed, Price's body language betrayed growing frustration, especially after missed chances at tops and double 10 to break Rock, only to see the young pretender polish off a double 8 to restore a three-leg lead.
With the Blackpool crowd sensing an upset, Rock continued to pile in the maximums, drawing clear at 15-11 after cleaning up 58 on double 20.
With the finishing line in sight, Rock produced a stunning 164 checkout - treble 19, treble 19, bullseye - to seal the match with the panache of a player utterly unfazed by the occasion.
Rock averaged 104.02 to Price's 100.21, hitting 10 180s and a high checkout of 164 in his victory.
"It's finally happened, so the whole world will be watching that game tomorrow night," Rock said after the win.
"Littler is one of my close friends behind the scenes. We're texting each other all the time, so I hope we're not too respectful and we both turn up. It's going to be a cracking game.
"Me and Littler are very, very close."
James Wade faces Jonny Clayton in Saturday's second semi-final after Littler and Rock duke it out in a best-of-33 legs duel.