The Blues ran riot on home soil, with Cole Palmer, Conor Gallagher, Noni Madueke and Nicolas Jackson on the scoresheet during a dominant performance against a disappointing West Ham.
Mauricio Pochettino's side have moved above Manchester United into seventh position in the table, now only two points behind sixth-placed Newcastle United with three games left.
Chelsea have made it successive wins in the league following their two-goal victory over Tottenham Hotspur on Thursday, and they have now only lost one of their last 11 matches in England's top flight.
A European finish has looked unlikely for some time, but the Blues are finishing the season impressively, and they will be looking for maximum points from their final three fixtures against Nottingham Forest, Brighton & Hove Albion and Bournemouth.
Cole Palmer moves onto 21 Premier League goals for season
West Ham, though, have now conceded 10 times in their last two league away matches, and the Hammers are without a victory in their last six matches in all competitions.
David Moyes is seemingly set to leave his position as head coach this summer, so his last two fixtures in charge of West Ham could come against Luton Town and Manchester City.
The breakthrough for Chelsea came in the 14th minute, and the identity of the goalscorer was no surprise, with Palmer scoring his 21st Premier League goal of a remarkable campaign.
The ball fell kindly for the Englishman inside the West Ham box, and he was never going to pass up the opportunity to bury the ball into the back of the net.
West Ham almost responded straight after, with Jarrod Bowen's effort coming off the crossbar, but Chelsea looked dangerous whenever they broke forward, and a second came for the hosts in the 30th minute, when Gallagher expertly volleyed the ball into the bottom corner after more lacklustre defending from the visitors.
The Hammers just could not deal with the pressure, and it became 3-0 in the 36th minute through Madueke, with the forward heading home at the far post after a knockdown from Thiago Silva.
Chelsea are ending the season in impressive form
Gallagher headed against the crossbar as Chelsea came close to a fourth late in the first period, before Bowen again struck the woodwork soon after for the second time in the contest.
There are likely to have been some raised voices in the West Ham dressing room at the interval, but the message was clearly not received, as Chelsea scored a fourth early in the second period through Jackson, who had the simple task of turning a low Madueke cross into the back of the net.
Bowen hit the woodwork for a third time in the 77th minute, with his effort being deflected onto the post, before Chelsea made it 5-0, with Jackson registering his second with a cool finish past Alphonse Areola.
Pochettino's side are now just six points off fifth-placed Tottenham Hotspur, so it has been some turnaround for a club that have been in crisis mode for stages of this season.
West Ham remain ninth in the table, only two points above 11th-placed Brighton & Hove Albion, so they could drop into the bottom half with a poor end to the season.