Mauricio Pochettino's side have now scored 22 times in their last six Premier League games at Stamford Bridge, and there was a fluency to their attacking play that could well have yielded substantially more than the five they put past the hapless visitors from across London.
Chelsea were three up at the break. First, Cole Palmer netted the 21st league goal of his debut season in west London, steering a loose ball into the corner, then Conor Gallagher volleyed home.
Noni Madueke headed the third near the end of an excellent first half, before Nicolas Jackson took his tally for the season to 13 in the league with a brace after the interval.
Chelsea climbed to seventh after recording back-to-back league wins for the first time since January, and there is increasingly the feeling that, after a difficult start, the players are responding to their head coach's methods.
For David Moyes' Hammers, this was a calamitous display. Eliminated from Europe and now all but out of the race to qualify again next year, it was hard to avoid a sense of a promising season petering out as the Chelsea goals flew past Alphonse Areola, and their players came to look more and more dejected.
Aston Villa's quest for Champions League qualification suffered a setback after Joao Pedro ended Brighton's six-match Premier League winless run with a dramatic 87th-minute winner.
Villa, who are juggling their top-flight commitments with a run to the semi-finals of the Europa Conference League, laboured for large parts of a tight encounter and were beaten 1-0 after Pedro headed home the rebound after his late penalty was saved by Robin Olsen.
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