The Kent side went into the break two-up thanks to strikes from former Gillingham player Danny Kedwell and Che Krabbendam.
The effervescent Ethan Prichard hauled Chi back into the contest with a goal of the season contender on 53 minutes before the Chats went further in front when Jack Evans converted a 57th minute penalty.
Ryan Davidson gave the Oaklands Park faithful hope with eight minutes of normal time to go but Ashley Nzala wrapped things up for the visitors sixty seconds later.
Miles Rutherford & Co made two changes to the team that lined up against Hythe last time out with Liam Montague coming in for the suspended Rob Hutchings at left back, and Kaleem Haitham returned to the starting XI in place of Callum Overton.
Chatham’s Reece Butler had the first bit of defending to do as he tidied up a Ben Pashley ping towards Prichard.
Lloyd Rowlatt then dallied a little too long laying the ball off to Prichard.
Chi keeper Kieran Magee was forced into a save with his feet after Krabbendam latched on to a pass that nicked off a Chi defender.
The away side won a corner a couple of minutes later that Joey Taylor swung in and Evans dragged an effort wide after the ball was cleared.
Prichard also pulled one off target at the other end following a neat move involving Joe Moore, Haitham and Rowlatt.
Nzala spurned a decent opportunity with a free header and Davidson bailed out Josh Clack, who got done down the left, with a superb tackle.
And then Davidson cut out Simon Cooper’s pass and fed Prichard only for the Chi No11’s attempt to brush the woodwork.
Next, referee Martin Bloor found himself surrounded by Chatham players protesting Montague’s challenge on Ike Orji – no card the decision.
Haitham’s cross on 20 minutes was headed away and Chats custodian Nathan Harvey got a glove on his follow up delivery.
And a nice piece of skill from Prichard in the subsequent attack gave him a chance to cut back but no one was there.
The visitors took the lead in the 26th minute when a ball through the middle undid two defenders and Kedwell slapped it underneath Magee.
Another opportunity came and went for Kedwell a minute later who wasn’t able to get anything like the same power on his shot and Evans’ swerving long-ranger gave Magee something to think about.
Intelligent play by Prichard got him past his marker only for fellow defenders to swarm around him.
Nzala got away with a clear push on Davidson but Connor Cody was there to make a crucial challenge.
Guilty of cheap turnovers at times Chi gave the ball up to Nzala on 34 who blazed an effort over the crossbar.
Cody then picked up a yellow card for a foul on the hard-working Nzala and Magee claimed Evans’ set-piece easily enough.
Clack chested a pass into Davidson’s path whose shot deflected off a defender for a 42nd minute City corner.
Rowlatt’s kick didn’t beat the first man and Chatham swiftly countered with Evans finding a seemingly offside Krabbendam who lashed in the Chats’ second goal.
Cody then cut out a square ball from Matt Bodkin to Krabbendam as the Kent team attacked once more and on the stroke of half time Davidson charged through and picked out Emmett Dunn for the Canadian to move it on to Clack who floated one over just above Rowlatt.
Pashley passed to Clack one minute into the restart but with Dunn shouting “Edges” just outside the box the Chi No9 sent in a wayward delivery.
Pashley then played a clever ball on to an overlapping Montague who won the hosts another corner which again failed to beat the defender at the near post.
And then Prichard grabbed Chichester a life-line with a spectacular overhead kick after Davidson got Clack in and Clack’s cross was acrobatically turned in beyond the hapless Harvey.
Chatham though restored their two-goal advantage some three minutes later when Davidson impeded Nzala in the penalty area and Evans thumped home his spot kick.
Prichard might have pegged the Chats back once more but after a silky touch and turn his shot on the swivel fizzed narrowly over.
Next, Davidson conceded a needless corner which Cooper headed powerfully against the bar.
On 65 minutes Nzala pulled a stunning save out of Magee as Kedwell teed him up.
The resulting corner was cleared at the front stick and Magee had a looping header to contend with.
City rang the changes with Olly Munt, Isaac Bello and Joe Clarke coming on for Haitham, Montague and Dunn.
Clack had a fierce cross blocked; Harvey denied Rowlatt; his defenders smuggled away another loose ball; and Davidson’s cross-cum-shot wasn’t far off.
Clack was then bundled over in the box – no pen according to Mr Bloor.
Chatham sub Callum Peck made a telling tackle to break up a promising move before Davidson smashed in a lovely 82nd minute shot.
Any hopes of Chi getting something out of the game went awry when Nzala made it 4-2 almost immediately from close range.
Prichard was fouled on the edge of the area by Butler but Munt’s free-kick was headed away and Harvey raced out bravely to claim with Bello bearing down on him.
Nzala won the visitors another penalty in stoppage time but Magee saved low to his left.
Chatham, who haven’t lost in the league at home this campaign, beat Chi 2-1 in the reverse fixture thanks to two goals in the last five minutes, and are the only team to do the double over Chichester in 2022-23.
The Chats move up to second place and Chi remain tenth with six games to go.
Miles Rutherford’s men are back on the road next away at basement club Corinthian on Saturday 25th March (Kick Off 3pm).
Chichester – Magee, Davidson, Montague, Moore, Cody, Pashley, Haitham, Dunn, Clack, Rowlatt, Prichard (Munt, Bello, Clarke, Weinberger).