The Blues took the lead through Antonio Rudiger as the German headed home following N’Golo Kante’s deflected shot after 55 minutes.
Chelsea manager Antonio Conte was sent to the stands following an argument with fourth official Lee Mason, as the Italian’s side were denied a corner.
A quiet opening 10 minutes ended as Mike van der Hoorn could have given away a penalty for holding onto Alvaro Morata inside the box but referee Neil Swarbrick waved away the protests.
Both sides enjoyed good spells of possession early on, but neither Thibaut Courtois or Lukasz Fabianski were really tested, which was a positive sign for Paul Clement.
Chelsea then began to dominate possession, and had three efforts from corners in quick succession, two coming from Morata and another a curling effort from Pedro but neither could get past Fabianski.
Fabianski was once again worked by Morata, tipping the Spaniard’s inventive volley over the bar as Chelsea inched closer and closer to taking the lead.
Morata has in fact scored more goals than the entire Swansea squad in the league this season. The Swans are the lowest scoring team in all of the top four English leagues, with just seven goals.
Like in the 0-0 draw with Bournemouth, Swansea clearly missed Tammy Abraham tonight as he was unavailable to play against his parent club.
Chelsea begin to dominate
The Blues’ best chance in the first half fell to Marcos Alonso as the wing-back had a free header from a corner, his effort was from a tight angle but couldn’t find the target.
Any momentum Swansea began to build was haulted by several wayward passes by Renato Sanches, who although was the only member of Clement’s side trying to create anything, had a very frustrating night on the ball.
Conte sent to the stands
Chelsea then could have taken the lead on the counter attack as Willian raced away before delivering a ball into the box that Alfie Mawson deflected behind, although the referee did not give Chelsea a corner.
That decision angered Conte so much that Swarbrick deemed necessary to send the manager off and into the stands just before half time.
Conte was shown red after getting in the face of the fourth official, his enthusiasm is often praised but this time it was deemed too aggressive towards the officials.
Second half starts as the first ended
Chelsea started on the front foot after the break, as Conte dictated tactics from upstairs where he saw his side win their eighth and ninth corners of the afternoon just minutes into the second half, but could not take advantage of either.
Both van der Hoorn and Mawson were in the right place at the right time on several occaisions, and are forming a very formidable partnership in Federico Fernandez’s unfortunate absence.
Van der Hoorn especially has vastly improved since Clement took charge at the club, and is unrecognisable from the timid, nervous defender that first moved to South Wales.
Willian then created a yard of space for himself to deliver the cross straight to Pedro, but the Spaniard was unable to convert as he sent his shot over the bar from 10 yards out.
Chelsea finally take the lead
However it was corner number 11 that Chelsea converted, as Rudiger headed into an empty net from six yards out.
Swansea were not switched on at the short corner, as Kante’s shot deflected into the path of Rudiger before the German defender was able to give the Blues the lead.
Chelsea nearly doubled their lead just minutes later, but Alonso’s goalbound shot was superbly blocked by the recovering Kyle Naughton.
The goal is in fact Rudiger’s first for Chelsea, and a hugely important one as the Blues look to stay in the title race.
Blues continue to pile on the pressure
Chelsea then began to find some joy down the right flank, as Davide Zappacosta, Willian and the goalscorer Rudiger often combined to create chances.
Fabianski was called into action once again, as Morata met Cesc Fabregas’ free kick but the Polish goalkeeper was able to tip his effort over the bar.
Morata was then sent through on goal, but Mawson was able to do enough to put him off as the striker lifted his shot over the woodwork.
Swansea were a bit more positive towards the tail end of the game, but didn't really trouble the Chelsea defence enough.
Eden Hazard then nearly created a goal moments after coming off the bench, but Morata was unable to convert the Belgian's cross.
Chelsea started the evening 11 points behind leaders Manchester City, with each win vitally important as the reigning champions look to make up the ground on the champions-elect.
While it was not a game Swansea expected to get anything out of, they have now lost eight of their last 10 games in all competitions, winning just once.
The Swans tonight equalled their Premier League club-record of four consecutive matches without a goal as they sit in 19th – only above Crystal Palace on goal difference.
As bottom club Crystal Palace gain momentum with just one loss in their last five games, and the three sides above Swansea prior to kickoff – Everton, West Ham and West Brom – recently appointing managers with sufficient experience in avoiding relegation, things are looking bleak at Swansea.