Chelsea took an early lead through Oscar before Swansea debutant Andre Ayew equalised on 28 minutes.
The visitors were level for just 90 seconds though as Federico Fernandez put through his own net.
Courtois was dismissed on 52 minutes for denying Bafetimbi Gomis a clear goalscoring opportunity. Gomis then equalised past substitute ‘keeper Asmir Begovic from the resulting penalty to complete the scoring.
Jose Mourinho issued a surprise with his team selection by naming Diego Costa in his line-up after earlier claiming the striker was still struggling with the hamstring injury that ruled him out of the Community Shield.
Costa scored a hat-trick against Swansea in the reverse fixture last season and he was closely guarded by Ashley Williams in the opening stages. However, that focus on Costa couldn’t stop Chelsea taking the lead on 22 minutes.
Oscar was the man to get the goal, fizzing in a cross-shot free-kick from the left flank which evaded everyone in the box and left Lukasz Fabianski a little flat-footed as the ball sailed past him into the far corner.
Swansea were more than matching the champions in the early stages and it wasn’t a big surprise when new signing Ayew equalised.
The lively Jefferson Montero made the hard yards down the left flank and floated a brilliant ball into the box that was headed at goal by Gomis.
Courtois made a fine save but Ayew was on hand to force home the rebound at the second attempt.
The teams were level for just 90 seconds though as Fernandez scored a very unfortunate own-goal.
Willian attacked the Swansea centre-back down the left flank and looked to send over a cross into the middle. The ball deflected off the defender and looped over Fabianski into the same corner where Oscar had scored.
The goal failed to deflate the Swans though, who came out all guns blazing after the break.
Jonjo Shelvey hit a post straight from a corner and Montero was denied from close range by Courtois before the goalkeeper was involved in the game-changing moment.
Gomis raced through on goal after being played onside by Willian and showed great pace to get to the ball before Courtois, who came flying out of his goal. There was clear contact on the striker and referee Michael Oliver was quick to point to the spot before brandishing a red card in the direction of the goalkeeper.
Begovic had the chance to be an instant hero in front of new fans but Gomis confidently stroked the ball into the net from 12 yards.
Swansea continued to press forward but Begovic stood strong to deny substitute Wayne Routledge from 15 yards.
Radamel Falcao was introduced for his Premier League debut for Chelsea but the best he could muster was a weak shot from the edge of the box that Fabianski saved with ease.
Saturday Night Football reaction – Jamie Redknapp
Swansea got in so many times behind the defence. The Chelsea defending was lax, it wasn’t sharp, it wasn’t aggressive. It’s the first day of the season so we don’t want to get too carried away but, in terms of the champions, that was as poor a performance as you could see. Chelsea scored nine goals against Swansea last season but today the body language didn’t seem right. It seemed very flat.
No doubt it (Courtois’ foul) was a penalty, but I don’t think he was denying a goalscoring opportunity, I don’t think it’s a red card and I think Chelsea are really unlucky. The ball was going away from goal and I believe Gary Cahill could get back on the line. There’s a chance he can score but I think the ball has to be going directly at goal. Maybe the referee thought it was dangerous play, I don’t think it was. Penalty absolutely, but I think a red card is extremely harsh.
Chelsea: Courtois (5); Ivanovic (6), Cahill (6), Terry (6), Azpilicueta (6); Matic (6), Fabregas (6); Willian (7), Oscar (7), Hazard (6); Costa (6).
Subs: Begovic (6), Zouma (6), Falcao (6).
Swansea: Fabianski (6), Naughton (6), Fernandez (6), Williams (7), Taylor (7), Ki Sung-Yueng (6), Shelvey (7), Sigurdsson (7), Ayew (8), Montero (8), Gomis (7).
Subs: Cork (7), Routledge (6), Eder (6).
Man of the Match: Andre Ayew