Chelsea kept their hopes of a top-four finish alive and dented Swansea City's survival bid with a 1-0 win at the Liberty Stadium.
In a game of precious few chances, it was Cesc Fabregas' superb fourth-minute strike that proved decisive – his 50th in the Premier League.
Andre Ayew curled wide for the hosts late on, but they rarely looked like finding a leveller against opponents who comfortably kept them at arm's length throughout.
The win lifts Antonio Conte's side just two points behind fourth-placed Tottenham, who face Watford at Wembley on Monday.
Swansea, meanwhile, are just one point ahead of 18th-placed Southampton following Mark Hughes' side's 2-1 win over Bournemouth earlier in the day.
Carlos Carvalhal's men now have three games to preserve their top-flight status, including home clashes with the Saints and Stoke City, in what promises to be a nail-biting climax to the season.
Swansea barely had a chance to catch their breath by the time Chelsea had raced into an early lead.
Eden Hazard showed characteristically quick feet to find space on the edge of the penalty area before teeing up Fabregas, who whipped a first-time effort with his left foot into Lukasz Fabianski's top corner.
Mike van der Hoorn got in the way of a goal-bound Victor Moses strike soon after, while Alfie Mawson clipped his own crossbar attempting to clear a loose ball as Chelsea dominated the opening period.
The Swans started to grow into the game towards the end of the half, but were unable to penetrate the Chelsea backline and test Thibaut Courtois.
50 - Cesc Fabregas has scored his 50th Premier League goal, becoming the third Spanish player to do so in the competition (after Fernando Torres and Diego Costa). Milestone. pic.twitter.com/P3FrLhaW6Y— OptaJoe (@OptaJoe) April 28, 2018
Swansea were successful in disrupting Chelsea's flow at the start of the second period but, much like in the first-half, they rarely looked like finding an equaliser.
Tiemoue Bakayoko dragged a shot wide from distance as Chelsea looked to double their advantage and put the game to bed, while Emerson Palmieri's low drive was kept out by Fabianski after the Brazilian had produced a dazzling run from just inside the Swans' half.
Moses then somehow contrived to prod wide from all of three yards after Fabregas' shot had careered towards him before Ayew missed the hosts' best chance.
The Ghanaian picked the ball up just inside the area, but his left-foot shot arced agonisingly wide of Courtois' post.
Tom Carroll flashed a shot wide and Wayne Routledge fired straight at Courtois in the closing stages as Swansea ultimately fell short of finding a priceless equaliser.
Key Opta Facts:
- Antonio Conte has won 50 of his 73 Premier League games in charge – only Jose Mourinho (63) and Pep Guardiola (69) reached 50 wins as manager in the competition in fewer games.
- Swansea have failed to score in 16 different Premier League games this season; in no campaign have they failed to score in more in the competition (also 16 in 2012-13).
- Chelsea have won three consecutive away league games for the first time since September (a run of five).
- Meanwhile, Swansea have lost consecutive league games for the first time under Carlos Carvalhal, last doing so in Paul Clement's final two games in charge in December.
- Cesc Fabregas' goal was his 50th in the Premier League, making him the third Spanish player to reach the milestone in the competition after Fernando Torres (85) and Diego Costa (52).
- Fabregas became only the fourth player to scored 50+ goals and register 100+ assists in the Premier League, and first non-British player to do so (Ryan Giggs, Wayne Rooney and Frank Lampard).