The first chance of the game came through a set-piece. Shaun Jeffers won a corner which Billy Knott was able to whip in - Chris Whelpdale then rose highest to head the ball home for 1-0.
Three minutes later, Chelmsford had their second of the afternoon. This time Jeffers won a free-kick, again floated in by Knott and this time found Sam Higgins who was also able to head beyond Tom Hadler to double the lead.
22 minutes in, City were well on top, almost adding a third when Jonny Giles worked a cross into the box but the Eastbourne ‘keeper was able to tip the ball away before it could reach Jeffers.
Having created the first two goals, Knott went close to adding a goal of his own after half an hour. Whelpdale’s cross found the creative midfielder, however his effort on the stretch was saved by Hadler.
Five minutes later, Eastbourne almost conceded the third when Hadler’s kick rebounded off Robbie Simpson before Jeffers’ shot was blocked.
Nick Wheeler then registered a shot for the hosts, however his effort travelled over without troubling Carl Pentney.
Borough were awarded a penalty two minutes later as Kristian Campbell fell under pressure from Barry Cotter. Greg Luer stepped up, but his strike went wide of the post to keep the score at 2-0.
Luer almost made up for that miss just before the break as he managed to get past Simpson and Mickey Spillane before curling an effort narrowly wide.
Simpson and City started the second half on top as Simpson headed over from a Knott corner.
The Clarets then earned themselves a penalty just 5 minutes after the interval when Spillane was brought down in the box by Roberto Nditi. Jeffers stepped up, sending Hadler the wrong way to extend the visitors lead to 3 goals.
Knott then fed the latest goalscorer, who ran at Manny Adebowale before shooting low at goal, allowing Hadler to save comfortably.
Eastbourne almost gifted City another goal with half an hour to play, giving the ball away before Jeffers teed up Higgins who forced a good save from Hadler.
The hosts were made to pay for their mistakes when they gave the ball away again less than a minute later. This time, Higgins punished them by drilling an effort from outside the box into the bottom corner to register his second, and City’s fourth of the day.
Higgins and Jeffers were next to combine before teeing up Whelpdale in the box but the wingers effort was saved well by Hadler.
Luer came close to getting a goal back for Eastbourne however his volley was blocked by Simpson and caught by Pentney.
With 5 minutes remaining, new loan signing Barry Cotter took aim from outside the box with the outside of his boot but his fizzling effort flew just over the bar.
Simpson was called into action with a goal line clearance in what proved to be the last chance of the game as he stopped West from grabbing a consolation goal for the hosts.