Jose Mourinho’s side twice had the lead, but paid the price for Courtois’ rash challenge on Swansea striker Bafetimbi Gomis as the France international raced through on the counterattack.
Referee Michael Oliver had no hesitation in producing a straight red card and pointing to the spot, allowing Gomis to beat substitute keeper Asmir Begovic from the spot and make it 2-2.
At Old Trafford, Spurs defender Kyle Walker handed all three points to United by steering the ball into his own net in the 22nd minute as he tried to tackle United captain Wayne Rooney.
It was one of very few chances in a scrappy match, which Louis van Gaal’s new-look United started with four preseason signings.
Sergio Romero was in goal after Van Gaal decided that Real Madrid target David de Gea was not in the right frame of mind to play. Fullback Matteo Darmain, along with midfielders Morgan Schneiderlin and Memphis Depay, all made convincing debuts, and Romero improved after some early signs of nerves.
The place to go for goals was Leicester, where former Chelsea coach Claudio Ranieri made an dream start to his return to the league after an 11-year absence.
Jamie Vardy struck first with a header after 11 minutes and Riyad Mahrez scored in the 18th and from the penalty spot in the 25th. Jermain Defoe and Steven Fletcher grabbed second-half goals for Sunderland, while Marc Albrighton got Leicester’s fourth to seal the points.
Bournemouth’s much-awaited game at Vitality Stadium was decided by Villa substitute Rudy Gestede’s header in the 72nd for last season’s FA Cup finalists. It was a frustrating day for the Premier League newcomers who dominated possession but misses the cutting edge quality you need to win in the Premier League.