Momentum swung this way and that with the hosts starting brightly – Josh Clack and Ryan Davidson scoring in the opening 15 minutes.
Lewis Jenkins pulled one back for the visitors 10 minutes before the break and then a worldie from Tom Biggs on 56 minutes levelled this quarter final tie.
Chi were reduced to ten men towards the end of normal time when Emmett Dunn got his marching orders but restored their lead through Callum Overton in the 112th minute.
Jarvis made it all square four minutes later and sent the Golds into the semi-final with a decisive final strike in an enthralling encounter on 120 minutes as George Gaskin and Mitchell Hand’s men added another dramatic chapter to Littlehampton’s extraordinary history-making season.
The FA Vase finalists have a trip to Wembley ahead of them, are top of the Southern Combination premier division, and also face Newhaven in the final of the Peter Bentley Challenge Cup.
Miles Rutherford & Co went with the starting XI that suffered an agonising late 1-0 loss last time out away at promotion chasers Herne Bay.
Here, the home side were out of the traps fast enough and went ahead thanks to a classy Clack sixth minute finish when Tyrone Madhani’s pinpoint cross from the left picked him out.
Chi keeper Kieran Magee came off his line swiftly moments later to deny Biggs before Ben Pashley cleared after Jarvis had an effort blocked.
Davidson then doubled the hosts’ advantage when he met Ben Mendoza’s delivery with a bullet header on 12 minutes, and it seemed Chichester were on their way once more in the competition they won in 2018.
Pashley pinged a pass to an overlapping Rob Hutchings who brought the ball down exquisitely but couldn’t find a teammate with a cross.
Next, Jarvis chested skilfully only to be clattered. Hand’s consequent set-piece some 25 yards out was tipped over by Magee for the first corner which came to nothing.
Magee then gave the ball away to Lucas Pattenden who fed it to Jarvis. The No11 didn’t get his feet right and a tame attempt did little to trouble the Chi custodian.
Kaleem Haitham had a shot blocked at the mid-point and Jarvis headed well wide at the other end.
A neat flick in an exchange between Biggs and Pattenden got Littlehampton into the box and earned another corner that Pashley headed clear before Magee got a strong glove on the follow-up.
Trickery from Biggs bought the Golds a free-kick which Hand took and defenders smuggled out for a corner.
Hutchings headed this away but the loose ball was lofted over and Jenkins snuck in to pull one back for the visitors. Offside? The referee’s assistant didn’t think so.
Jarvis spurned the first opportunity of the second half when his mishit effort drifted wide and then pressurised Magee to skew the ball out for a throw.
Ethan Prichard opened up Littlehampton five minutes in but was guilty of a poor final pass.
Chi had penalty appeals turned down by Mr Small as Jordan Clark appeared to handle – a corner awarded instead.
Madhani’s first kick was cleared and the follow-up whipped in too deep.
Hutchings hooked a shot off the line after Biggs drove into the area and then the same player caught Magee out with a sublime long-ranger to make it 2-2 and send the Golds fans behind the goal into raptures.
The visitors now had their tails up and might have won a spot-kick on the hour mark when Pattenden was clipped in the box.
Overton came on for Madhani, and Liam Humphreys replaced Jordan Layton as both teams freshened things up.
Former Chi player Rory Biggs found Lee Garnham in a dangerous position only for Davidson to hack away.
Silky skill from Mendoza allowed him to spray a ball to Hutchings who charged down the left flank. His cut-back was turned out for a corner that wasn’t capitalised on.
Davidson blocked Pattenden’s shot and Prichard didn’t get enough on his 70th minute attempt.
Pattenden then should have given his side the lead after he picked a pass only to pull a shot wide.
Biggs and Pattenden combined in the next attack and forced a corner which Garnham headed over.
And then came one of the game’s key turning-points as Dunn saw red in the 84th minute.
What had the ref seen?
Despite protests from players and the dugout, the Canadian became the fifth Chi player to walk since the turn of the year.
Hand struck the resulting free-kick into Magee’s gloves.
With a couple to go Gaskin fired over and Humphreys flashed a header off-target before Lewis Hyde received a yellow for impeding Jarvis.
And so, we went into extra time.
Mendoza won a 97th minute corner which Hutchings took and defenders headed away.
Hutchings was then bundled over by Garnham who got a yellow for his troubles and dual-signing Declan Seiden joined Garnham in the notebook moments later for a foul on Humphreys.
Biggs fizzed one into the side-netting before Davidson’s determined run through the centre of the park led to a pass to Overton who mishit his subsequent ball.
Garnham glanced a harder-to-miss header wide early in the second period of the 30 additional minutes before Garnham ballooned a shot over the frame of the goal as the game opened up.
An unfortunate slip at the back on 112 presented Overton with a chance which he gratefully accepted to put Chi in front again with his 15th goal in all competitions.
The ref wasn’t interested in penalty appeals as the Golds pressed but the hosts’ lead lasted barely four minutes as Jarvis made it 3-3 from close range.
Magee pulled off the save of the night to deny Gaskin and with a shoot-out looming Jarvis grabbed the winner in the 120th minute.
Littlehampton, battling on four fronts, have other fish to fry, whilst Chi now have just three league games left of an up and down season.
Chichester welcome East Grinstead to Oaklands Park on Friday 15th April (Kick Off 7:45pm) before travelling to Burgess Hill Town on Monday 18th April (Kick Off 3pm).
Chichester – Magee, Davidson, Hutchings, Dunn, Hyde, Pashley, Prichard, Mendoza, Clack, Madhani, Haitham. Subs: (Glenn, Oakwell-Boulton, Mockford-Allott, Seiden, Overton)