Chelsea skipper John Terry put through his own net early on, but Costa continued his recent positive form by completing his hat-trick in a 22-minute spell.
Here, Sports Mole has looked back over the contest to determine if the result was a fair one, or whether the Swans can feel hard done by.
On target: 9
On target: 2
Was the result fair?
Over the course of the 90 minutes, Chelsea were deserving victors. They may have started the contest relatively slowly, but as the first half wore on, they started to take control of proceedings and could have in fact won by an even greater margin had they taken their chances in the closing stages. Swansea certainly played their part, though, and were by no means a pushover. They did not deserve to lose by any more than a two-goal margin.
There is every chance that Jose Mourinho would not have been a happy manager during the break. Costa had equalised just before the interval, but his side had been poor in possession and had given the visiting defence and midfield far too much time in possession. That changed after the restart, with the likes of Eden Hazard and Cesc Fabregas showing just how creative they can be as a duo. They loaded the bullets for Costa, who is in deadly form at present.
However, one note of caution for Mourinho and his coaching staff will be the amount of goals that his side are conceding at present. That's now five against in two games and with Manchester City next up in the Premier League, they will need to tighten up.
For 30 minutes, Garry Monk's men played their hosts off the pitch. Their passing was slick and when they did not have the ball, they hounded Chelsea into making mistakes. A Chelsea onslaught was inevitable and the goal just before the break proved to be the turning point, with Swansea penned back for most of the second half. Even so, they kept going and even got a late consolation, which they deserved because a 4-1 scoreline would have been harsh. There is no need for Monk to be too despondent because against lesser teams, as they have shown already this season, Swansea will pick up more than enough points to stay in the Premier League.
Sports Mole's man of the match
Diego Costa: He may not have been involved in everything Chelsea did, but without him, they probably would not have won this match. The Spaniard can be anonymous for a long while and then he will pounce, just as he did for the goal that completed his hat-trick. With seven goals in four games, is there a more in-form striker in world football right now?
To be fair to Terry, there was not too much that he could do with the own goal, but that doesn't get him off this award! Any own goal is always amusing for the neutral and this was no different. He seemed to get his feet muddled up and before he could correct them, he had diverted Neil Taylor's cross into his own net.
Kevin Friend dished out three yellow cards to Swansea players, but, in fairness to the official, each one of them was warranted. Aside from that, it was a relatively straightforward encounter for the referee to take charge of, although he does deserve credit for not trying to be the centre of attention and allowing proceedings to flow freely.
Chelsea: The Blues turn their attention to the Champions League on Wednesday night with the visit of German side Schalke 04 to Stamford Bridge.
Swansea: As for the Swans, they return to the familiar surroundings of the Liberty Stadium next weekend when Southampton make the trip to Wales.