Ollie Smith’s side had edged to a 31-28 victory at Sudbury a week earlier and, after a quiet start, they opened the scoring with a try from Teddy Hepworth on 17 minutes.
Sean Mullins raced in for an excellent second try, with Charlie Fatoma adding the conversion to make it 12-0.
The visitors opened their account with a penalty, but Barking replied almost immediately as Joseph Cook ran through the middle and Fatoma finished off the move in the corner.
Chelmsford slotted another penalty, then pounced on loose ball to run in their first try, which was converted to close the gap to four points at half time.
But Barking were soon back on the attack after the restart and Samuel Wamala touched down for their fourth try to clinch a bonus point, with Fatoma’s conversion making it 24-13.
The visitors would not surrender easily, claiming their second converted try of the afternoon to cut Barking’s lead to just four points once more.
But Fatoma ran under the posts for his second try, which he also converted, and then added a penalty to make it 34-20.
And Fatoma repeated the trick to complete his treble with another try under the posts, which he also converted, before Nathan Barham intercepted a Chelmsford pass and ran between the posts for another converted try.
Barking brought up their half-century as scrum-half Conor Baker touched down in the corner, with Fatoma adding another conversion to complete a personal haul of 30 points.
And the big win will have given Barking a notable boost as they now take a break from league action, before returning with a trip to Old Priorians on October 22
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