There were early chances for both teams.
Chichester keeper Steve Mowthorpe was forced into a save in the second minute and Lloyd Rowlatt’s shot was diverted for a corner at the other end.
Clack then picked out Ryan Penny who was fouled and the hosts’ stopper did well to get down to Matt Axell’s low free-kick.
Ben Pashley next linked up effectively with Tafadzwa Kanjanda but Rowlatt’s effort was cleared over the bar by a defender.
A curling shot from Axell crashed against the post on 10 minutes before Penny had an attempt blocked following tricky play by Clack.
And moments later the Chi No 10 got a flick on a Mowthorpe clearance that sent Rob Hutchings away.
Clack and Hutchings were then involved in a slick move only for Ryan Davidson to drag a shot off target before the Chi right back went close from a Rowlatt corner.
The Hampshire side got in on the half hour mark after Rowlatt was muscled off the ball only to shoot wide.
A measured pass by Haitham found Axell who drove into the box but lost his footing as he looked for a teammate.
Haitham then went on one of those characteristic mazy runs but Baffins countered and there was a bit of a mix up between Mowthorpe and Ryan Peake who went for the same ball.
Clack and Hutchings forced a couple of opportunities with the break approaching before some calm defending by Pashley denied the home side and Mowthorpe pulled off the save of the half palming a smart shot away.
The second period, like the first, featured chances for Baffins and Chi in the opening minutes.
Rowlatt had another shot blocked and Mowthorpe’s acrobatic stop was tidied up by Pashley.
Then one of the back four got a touch on Penny’s effort and deflected the ball out for a corner that came to nothing.
Corey Heath and Emmett Dunn replaced Peake and Rowlatt eight minutes in as the Sussex club changed things up.
A drive through midfield by Axell resulted in Penny forcing a corner before Haitham’s cross was hooked clear.
Prichard came on for Hutchings up front in the 57th minute and was involved with his first touch when a lovely turn and a burst of pace forced a defender to concede a penalty which Clack converted.
The hosts had appeals for a spot kick of their own turned down sixty seconds later.
Miles Rutherford and Graeme Gee brought on Flori Vucaj, Connor Cody and Sam Ndlovu for Davidson, Pashley and Penny and the visitors doubled their advantage on 64 minutes with an excellent finish by Prichard after a Haitham run.
Haitham then played Clack in but the keeper just got to the ball ahead of him.
Chi forced a series of corners and Clack made it 3-0 from one of these getting the last touch in a goalmouth scramble to prod the ball home after a powerful Dunn header.
Baffins pulled one back before Haitham sealed the win late on with a crisp drive in off the post.
Chichester travel to Alford on Saturday 29th August before welcoming Worthing and Bognor to Oaklands Park next week.
Chichester – Mowthorpe, Davidson, Kanjanda, Axell, Peake, Pashley, Rowlatt, Penny, Hutchings, Clack Haitham. Subs – (Dunn, Cody, Heath, Pricard, Vucaj)