The Blues, who surrendered their league lead with a 3-2 loss to West Ham United last weekend, trailed early from Raphinha’s 28th-minute penalty.
But Mason Mount squared it up before half-time with Jorginho scoring a penalty in the 58th minute, only for Leeds to level in the 83rd minute from Joe Gelhardt.
Chelsea, though, won a fortunate injury-time penalty after a Mateusz Klich foul on Romelu Lukaku, which Jorginho coolly converted.
Leeds boss Marcelo Bielsa wouldn’t be drawn into discussing the penalty, but said: “It was a game we deserved to draw and we lost it when it was finishing. That increases the disappointment.”
Meanwhile, Chelsea boss Thomas Tuchel said: “We deserved to win but of course we were a bit lucky to score a goal so late into injury time.
“Im very happy because we came back twice from conceding equalisers and showing that sort of character is very impressive. We turned things around, which really pleased me.”
Elsewhere all the top English clubs won on Saturday, with Manchester City getting past 10-man Wolverhampton 1-0 thanks to Raheem Sterling’s 66th-minute spotkick. Raul Jimenez was sent off for Wolves.
Liverpool also needed a penalty to get past Steven Gerrard’s Aston Villa 1-0, with Mohamed Salah scoring the winner.
Cristiano Ronaldo fired in a winner from the spot as Manchester United won 1-0 at Norwich, while Arsenal beat Southampton 3-0.