VCD, who thumped Chi 3-0 in the reverse fixture on the opening day of the season, went ahead here after the break through Youssef Bamba but Overton equalised in the 77th minute before sealing the come-back win late on.
City boss Miles Rutherford praised the spirit in his Sussex side following their dramatic win over league leaders Ashford United last time out where Scott Jones came off the bench to score an 87th minute winner in a five-goal thriller and knock the Nuts and Bolts off top spot.
And Chichester had to draw on that spirt again in an enthralling end-to-end first half and a more physically intense second one played on a pristine surface.
Rutherford & Co went with the same starting XI that faced Ashford, so Jones was on the bench with Kaleem Haitham, Lewis Hyde and Charlie Oakwell-Boulton and Eric-Georges Dellaud from the U23s.
Both teams probed in the early exchanges.
Lloyd Rowlatt, Rob Hutchings, Emmett Dunn and Tyrone Madhani moved the ball about nicely only for Overton to stray offside.
Hutchings then intercepted but Madhani’s flick towards Overton didn’t come off and the subsequent pass was inaccurate.
Chi’s left back next conceded the first corner which Chris Edwards took and Hutchings cleared.
Dunn and Jamie Horncastle had to have their wits about them but the Canadian got in firmly and skipper Horncastle powerfully headed away.
Ben Pashley, Hutchings and Madhani got something going on the left wing but Hutchings’ cut-back was cut out.
Ethan Prichard tried his luck with the first shot of the game after a neat piece of skill in the build-up only for a defender to block.
Prichard was then involved with Hutchings when another effort was bravely covered and Dunn could only manage an air-shot.
Anthony Adesite, scorer of Vickers’ third goal at Oaklands Park back in August, combined with Edwards for a cross that Horncastle dealt with.
At the other end, Ben Mendoza tried to play Prichard in down the right but overhit his pass.
Adesite and the impressive Ayman El-Mogharbel exchanged a quick one-two for a shot that wasn’t far off.
Lovely play by Horncastle instigated a counter-attack where Madhani teed up Hutchings with a fierce attempt that Vickers captain Sam Mott got a strong glove on.
Madhani’s set-piece moments later was headed away and then Pashley did the same with another Edwards corner kick.
A cracking chested pass by Overton to Madhani helped Chi break once more but it fizzled out on the right hand flank.
Rowlatt dragged an effort narrowly wide at the mid-point and one by Dunn nicked off a defender and into Mott’s arms.
Kieran Magee wasn’t really troubled by Edwards after Adesite did Hutchings and Pashley cut out a cross-field ping intended for El-Mogharbel
Adesite then bullied Madhani off the ball but teammates bailed him out and Hutchings found Prichard who delivered it towards Overton, however, the No9 couldn’t get a decent connection.
Ryan Davidson defended brilliantly to deny Bamba on the half hour mark and Adesite had a go with an attempt that Magee kept in play.
VCD pressed again and won a corner this time. Bamba whipped this one in but it came to nothing.
Chi earned one of their own after Hutchings’ free-kick deflected off a defender following a soft foul on Mendoza only for Madhani to cross too deep.
Dunn cut out a pass from Edwards to Bamba and moved the ball on to Mendoza who fed Rowlatt. The mercurial midfielder then set up Hutchings for a shot which was blocked.
Things heated up a bit five minutes before the interval amid some inconsistency, with some fouls being given and others not.
El-Mogharbel received lengthy treatment following Madhani’s tackle and Dunn headed a Prichard cross over the bar before a slick move involving Dunn and Mendoza got Prichard in but the forward lifted his shot and was offside anyway.
A lively second half saw rejuvenated hosts trying to out-muscle their opponents.
Horncastle remained composed to deny El-Mogharbel and then Magee was out swiftly ahead of an onrushing attacker.
Chi defenders managed to steer Jason Williams’ effort away for a corner but fell behind six minutes in when they failed to clear their lines.
The ball popped up nicely for Bamba who pulled the trigger and beat Magee at his near post.
This fired Vickers and a well-timed tackle got them on the break again only for Magee to make two excellent saves in as many minutes to keep his team in the contest.
Bamba, who posed a real threat down the left wing, drove again against Davidson but fellow defenders snuffed out the danger.
Haitham replaced Madhani as Chi changed things up just before the hour. And Haitham, along with Jones who came on for Prichard, would both make an impact on the outcome of the game.
A catalogue of niggly fouls were exchanged with both sides spurning set-piece opportunities as things petered out for a spell.
Magee headed calmly away from Williams before Overton was inches off a lovely ball into the box.
Odd scenes ensued after a tackle on a Chi forward and a coming together of Dunn and Charles Etumnu with referee Peter Conn and his assistants having to deal with protests from a cluster of players.
Dunn and Etumnu were both cautioned and things got back underway.
Vickers might have capitalised on a Magee mistake when he gave the ball away and then made another awkward clearance of sorts when it bobbled up again.
Bamba wasted all his hard work down the left following a lovely jinking run with an awful shot.
And then Overton gave the visitors a lifeline when his effort crashed in off a post after some battling from Rowlatt and a super cross from Haitham.
VCD should have retaken the lead but Magee pulled off another fine stop, with his feet on this occasion, from point-blank range.
Next, Jones linked up with fellow sub Haitham to earn a corner that Mott punched clear.
Horncastle drew a foul out of Marcus Elliott and then Jones did well to win a throw-in just before his downward header from Hutchings’ free-kick bounced into Mott’s hands.
Overton bagged the winner in the 84th minute, his 10th goal in all competitions this season, guiding in a measured cross by Hutchings after a superb ball out to Hutchings from centre back Horncastle.
The visitors endured five minutes of time added on to record a second away league win this season and leapfrog VCD in the table.
A run of five victories, two draws and one loss in the past eight Isthmian south east games has moved Chichester up into eighth place.
Miles Rutherford’s men welcome a Brighton & Hove Albion side to Oaklands Park for the re-arranged Sussex Senior Challenge Cup tie on Tuesday 14th December (Kick Off 7:45pm) and are back in league action at home to Faversham on Saturday 18th December (Kick Off 3pm).
Chichester – Magee, Davidson, Hutchings, Horncastle, Mendoza, Pashley, Rowlatt, Dunn, Overton, Madhani, Prichard. Subs: (Jones, Hyde, Oakwell-Boulton, Haitham, Dellaud)