After scoring the late goal that sent the Blues into the Champions League semi-finals on Tuesday, Ba netted the only goal of the game midway through the second half at the Liberty Stadium today.
Here, Sports Mole casts its eye over the action in South Wales.
On target: 4
On target: 3
Was the result fair?
Only just. After Chico was sent off so early, it should have been a walk in the park for title challengers Chelsea. They just about came through, but it was hardly convincing from Jose Mourinho's side.
Garry Monk will be so proud of the way his side played after being reduced to 10 men. Ultimately, they didn't take the half-chances that they had and it always felt like Chelsea would break through. That doesn't mean that Monk won't be annoyed with the way that Ba's low shot squirmed under Michel Vorm's body. Should have been saved by the Dutchman.
Three points. That's all that matters to Mourinho and Chelsea but it wasn't a great display. As you can see from the stats above, Chelsea managed to get just three of their 26 shots on target. Once again it was Ba who made the difference and Samuel Eto'o didn't show much when he came on to suggest that he should start the next game. Mohamed Salah saw a lot of the ball but his decision-making was often wrong and he also missed a couple of great chances in the first half.
Sports Mole's man of the match
Demba Ba: Not one single player stood out so it's only right that we credit the match-winner here. Ba scored the all-important goal and worked hard for the 79 minutes that he was on the pitch.
Eto'o should have definitely put Chelsea in front 10 minutes before Ba struck when he was presented with a golden opportunity 10 yards out. All the Cameroonian really had to do was hit the target but he snatched at the chance and dragged it embarrassingly wide.
For the most part, Phil Dowd had a good game. However, his sending off of Chico was harsh. The Spaniard's first cynical foul was definitely worthy of a caution but the second trip on Andre Schurrle might have just been a foul.
Swansea: The Swans now have a relatively easy run-in and next go to floundering Newcastle United on Saturday.
Chelsea: The Blues, meanwhile, travel to rock-bottom Sunderland on Saturday ahead of a huge week where they face Atletico Madrid in the Champions League semi-finals either side of a ginormous trip to Liverpool.