The Cherries scored all four of their goals in the second half. The visitors scored their first goal on 53 minutes and they then doubled their lead on 75 minutes.
With only eight minutes of the 90 left, Bournemouth scored the third goal of the game and in additional time, the away side made it 4-0.
The first chance of the match came for the visitors when they won the first corner of the game, but Eloise Williams was there for Chi to clear it away from danger.
Minutes later, Chichester won their first corner. It was played into a dangerous area by Morgan Bond, but it was headed wide.
Katie Long got a shot away on the edge of the area that was straight at the opposition goalkeeper who gathered it well.
On 11 minutes, Charlotte Long turned well and fired a shot just wide of the post.
Captain Gaby Hobday did well on the right to beat the defender and win a corner which unfortunately came to nothing.
A lot of the play was happening in the middle of the pitch, with both sides doing well defensively and limiting each other to very few chances.
A long free-kick into the Chichester 18-yard box was headed away well by Aimee Boxall and Lisbeth Mottashed was there to clear it away fully from danger.
Early in the second half, Hobday did well to get past two defenders and get herself into a shooting position, but her shot towards goal was blocked.
On 52 minutes, a mix up at the back allowed the attacker to nick the ball from the Chi defence and her lobbed effort landed on the roof of the Chichester net.
Only a minute later, Bournemouth took the lead. The Cherries’ first shot hit the post and rolled away from the goal, but they continued the attack and a shot from the middle of the box found the bottom corner.
The away side continued to press, and a long-range effort went narrowly over.
Chichester were looking for an equaliser, and on 69 minutes Mia Gardner played a brilliant pass through to Hobday and Maya Butler, but the defender just managed to poke it away from the Chi attackers who would’ve been through on goal.
However, on 75 minutes, Bournemouth doubled their advantage. The attacker got past the Chi defence and curled an effort beyond Chloe Simmonds into the net.
Five minutes later, Simmonds’ kick out fell to a Bournemouth player whose first-time shot was on target, but the Chi goalkeeper was quickly back on her line to make the save.
With eight minutes of the 90 remaining, Bournemouth looked to have sealed the win as they made it 3-0.
In additional time, the visitors scored their fourth. Simmonds saved the first shot, but the attacker was first to the loose ball and she tapped it in.
Next up for Chichester City Women is a trip to Abbey Rangers on Sunday 6th March.
Chichester City: Simmonds, Mottashed, Andrade-Paris, Collins, Williams, K.Long, Hobday, Boxall, Bundy, M.Bond, C.Long
Substitutes: Gardner, C.Bond, Verrinder, Butler