Playing in the shadow of the earlier Liverpool game that had put the Reds five points clear at the top of the table, Chelsea knew only a win would keep them in title contention.
After wins on Saturday for both Fulham and Cardiff City, Swansea had been pulled back into the relegation battle.
The match started quite uneventfully until upon receiving his second yellow card Swansea defender Chico Flores was sent off.
Despite playing against 10 men Chelsea took almost 50 minutes to break through the home side with a Demba Ba strike.
Chelsea continued to create chances but Ba’s was the only goal of the match so Chelsea stay second, two points behind leaders Liverpool while Swansea are three points from the drop.