Jackson needed just 18 minutes to breach a porous West Ham defence twice, breaking in behind to produce two composed finishes and leave the hosts with a mountain to climb.
Julen Lopetegui's team briefly improved before half-time but their hopes of a comeback were dashed by Cole Palmer's strike almost immediately after the interval.
While Chelsea are now unbeaten in four league games and sit second in the early-season standings, West Ham remain 14th with four points ahead of Saturday's other fixtures.
Jackson caught West Ham cold with the opener inside four minutes, slotting his finish through Alphonse Areola's legs after being played in by Jadon Sancho, who was making his first Chelsea start after assisting Christopher Nkunku's winner at Bournemouth.
He had his second 14 minutes later, finishing with the outside of his boot after receiving a pinpoint throughball from Moises Caicedo, then he turned provider as the Blues killed the contest early in the second half.
Just 68 seconds after the restart, Jackson scampered over halfway with the home defence retreating, then teed up Palmer to crash his finish into the far corner and cap an enjoyable outing for Maresca's side.