The victory, Chelsea's 28th of the season, put the long-time league leaders 10 points clear of second-placed Tottenham Hotspur, who have only three games left to play.
Substitute Michy Batshuayi's late goal clinched the English Premier League title for Chelsea as they beat West Bromwich Albion 1-0 on Friday but they were made to fight all the way for the victory they craved at The Hawthorns.
Chelsea were suffering late nerves as West Brom threatened to prolong the title race but Batshuayi prodded home the winner after 82 minutes to spark wild celebrations from Chelsea manager Antonio Conte.
The victory, Chelsea's 28th of the season, put the long-time league leaders 10 points clear of second-placed Tottenham Hotspur, who have only three games left to play.
Italian Conte is only the fourth manager to win the Premier League title at the first attempt, emulating his Stamford Bridge predecessors Jose Mourinho and Carlo Ancelotti as well as Manuel Pellegrini who achieved the feat with Manchester City.
Conte, who won three consecutive titles as Juventus manager before taking over the Italian national team, danced for joy with his players in front of Chelsea's travelling fans as the final whistle blew on a tense night in the Midlands.
Chelsea have now won five Premier League titles since Russian billionaire Roman Abramovich bought the club in 2003, but this one is arguably the most impressive considering they finished a woeful 10th last season.
"You have to cherish these moments, you work so hard all season to be where we are. Consistently we have been the best team in the league. There is no better feeling in football," Chelsea defender and stand-in captain Gary Cahill told Sky Sports.
"People have written us off as a team and individually and this has shut them up. We are champions. It's another one in the cabinet."
It was not vintage Chelsea but they got the job done.
They dominated possession against eight-placed West Brom who had little to play for but pride and rained in shots before halftime, Cesc Fabregas and Pedro going closest.
West Brom offered the odd counter-attack but the one-way traffic continued as Victor Moses was denied by a splendid low save by Ben Foster.
Eden Hazard had another effort blocked on the line but as Chelsea strained for the winner they began to look a little vulnerable at the back to West Brom counter-attacks.
The visitors had a huge scare when Salomon Rondon burst clear but his effort was superbly blocked by Cahill.
In the end Chelsea owed it to misfit Batshuayi, a peripheral figure for most of the season, to win it with only his second league goal since joining the club.
Six minutes after replacing a tiring Pedro, the Belgian striker signed from Marseille for 33 million pounds ($42.5 million), stuck out a leg to convert Cesar Azpilicueta's cutback despite a valiant attempt by Ben Foster to keep it out.
The final minutes were interrupted by some scuffling in the stands but nothing could dampen Chelsea's joy.