The Whites fell to defeat in heartbreaking fashion in the Premier League at Stamford Bridge on Saturday afternoon.
Leeds travelled to the capital depleted but showed huge fight and went ahead from the penalty spot through Raphinha after Dan James was sent tumbling by Marcos Alonso.
The hosts turned the game around and went ahead on the hour due to a penalty of their own but Marcelo Bielsa's side levelled up the game once more through substitute Joe Gelhardt in a stunning cameo.
Joffy, as he is affectionately known, burst into the area to smash home a Tyler Roberts cross with his first touch seven minutes from time.
United, though, were hit with an injury-time loss with Chelsea again winning a spot-kick in the third minute of added time which Jorginho duly converted for his second.
Mateusz Klich was the guilty party as Antonio Rudiger was sent to the floor for a second time after winning the earlier 12-yard dead ball amid Raphinha's clumsy slide tackle.
The defeat sparked furious scenes post-match as both sets of players came together at the full-time whistle amid Blues celebrations in West London.
"I was confident we could get one more chance. In between [the goals] we played a little bit with some fear where we have something to lose," Tuchel said post-match.
"It's a bit of luck in the end when you get a late goal. We needed this win, desperately for the mood. It was a nice game of football. Very intense and I'm very happy with how we played.
"I think we deserved to win but of course it's lucky when you have a late goal in extra time. But coming back twice is very impressive and I'm very happy we turned things around. It was tough work but we didn't expect anything else.
"We were lucky, we needed this. We were unlucky in the last two games conceding very late goals so maybe this is exactly what we needed. They are a strong team. They hate to lose like we do.
"It's not so easy two score two penalties. I wasn't sure if he [Jorginho] would take the second one. We believe in our players, it's not easy so full credit to him."
Tuchel added: "There's no alternative to winning in this dressing room. We have two days off now as we play again on Thursday. I'm really happy for the team and the staff that we have these two days with a feeling that we have turned things around.
"There are things to improve as always but I'm very happy with the result."
On the bust-up between the two sets of players at the final whistle, Tuchel said: "I didn't see any of it. I was focused on the match. Emotions were boiling. I think it's normal. I didn't hear it was anything serious so all was good."