The visitors looked far more intent on staying in the competition, writes Chris Pickett.
Hosts Havant fielded a weakened side and they ended up being outplayed.
Chichester's determination and their extra attacking quality paid off on the day as they marched through to the next round.
Prior to Havant taking the lead there were early chances for both teams, the majority falling to Chichester.
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And on one occasion an outstanding save by Maciej Pacanowski kept the visitors off the score board.
Havant struck first from their first penalty corner in the 19th minute when Federico Bertoni found a defender's foot on the line just inside the post,Â which deflected the ball into the goal.
After scoring, Havant had a period of possession but it was Chichester that equalised in the 28th minute.
An attacker was fouled at the top of the circle and a penalty stroke was awarded. This was neatly tucked away.
Chichester had further opportunities to go into the half time break in front after a deflected shot hit a Havant post and a late Chichester penalty corner in the 35th minute was well saved by Maciej.
Andy Sparsholt put Chichester ahead in the 47th minute after he deflected a cross from the side line past Maciej and Chichester scored again in the 55th minute from their second penalty corner of the game. A slip flick at the top the circle rebounded off the keeper's pads and the rebound was slapped into the Havant net.
Havant tried to cut the deficit as they went in search of goals and were determined not to give up.
But Chichester were in no mood to relinquish their lead.
They defended resolutelyÂ to eventually give them a deserved win and entry into the next round.
Meanwhile, fellow National League men's conference west side Fareham were knocked out on penalties by Team Bath Buccaneers.
The teams drew 4-4 after Fareham fought back from 4-1 down to level the tie.
On penalties Bath earned a 4-3 success as they booked their place in the next round of the competition.
Fareham's next league match is also at Team Bath. This game takes place after the break for Christmas and new year.
The teams return to league action on February 3.
Havant will be in action at Isca when they make their return to league action.