The visiting Swans actually broke the deadlock when John Terry put through his own net, but parity was restored just before the break by Costa.
The summer signing from Atletico Madrid then made sure of the outcome by adding two further goals, before his replacement - debutant Loic Remy - scored a fourth. Jonjo Shelvey pulled one back for Swansea in the closing stages, but it didn't deter from the fact that it was Costa's day.
You can find out how the match unfolded with Sports Mole's minute by minute text updates below.
"They are one of the powerhouses of the league. They have quality players over the pitch. When you analyse them, there are a lot more strengths than weaknesses.
"They can hurt you in many areas via different players. They'll be favourites for the title this season. There's always a plan, every team in the world is beatable. We have to give our best performance in order to warrant winning any points. We have to go out there, be ourselves, be confident and hope it's good enough to get the points."
"Swansea have a good team. They had a good team [last year and] they've had a good team for a couple of years, since they were promoted to the Premier League. They've always represented themselves in the Premier League with a good team, playing good football for a while.
"They have good players and I don't think they've lost any good players. If they lost any, they weren't important players. They bought, bought well, and invested seriously buying quality players.
"They did well to keep their good players and bring others in to improve them. They are doing very well and for Monk to win the manager of the month is deserved."
VINE: The build-up continues to kick-off at Stamford Bridge. https://t.co/YAfvSSdiY4— Swansea City FC (@SwansOfficial) September 13, 2014
Swansea!!!! Get in. This team give me great joy when I watch them. They play with belief home and AWAY. FOOTBALLING TEAM— Rohan Ricketts (@RohanRicketts) September 13, 2014
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