Willian was dismissed for the Blues for a second yellow card and then Villa struck with eight minutes remaining.
Delph made a surging run through the middle before picking out Marc Albrighton down the left. The winger's return ball was delightfully flicked into the far corner thanks to some sublime improvisation by the midfield man to give Villa a morale-boosting victory.
Ramires was shown a straight red by referee Chris Foy for a late challenge on Karim El Ahmadi and then Mourinho was sent to the stands as Villa dented the leaders' title hopes.
The result means Chelsea surrendered the initiative to Manchester City.
Manuel Pellegrini's men, who beat Hull in the lunchtime kick-off, are six points behind Chelsea, but the fact that they have three matches in hand makes them favourites.
Tempers threatened to boil over - just like they did in the reverse fixture - early on when Nathan Baker clattered into Fernando Torres and received a booking in the fourth minute.
Willian received a yellow soon after for an equally poor challenge on El Ahmadi.
It was Christian Benteke who created the only real chance of the first half when he turned and smacked a low volley an inch wide of Peter Cech's goal.
Nemanja Matic thought he had given Chelsea the lead just before the break, but Foy correctly chalked off the midfielder's tap-in as he handled the ball before shooting.
Those Villa fans who had not escaped early for a half-time pie held their breath in injury time as Joe Bennett took out masked man Ramires as he raced through, but Foy flashed a yellow card when Mourinho, gesticulating angrily on the touchline, clearly wanted a red.
The intensity of the game improved in the second half and Chelsea were the main protagonists.
Brad Guzan clawed the ball off his own line following a mis-cued clearance from El Ahmadi. Guzan then got down well to deny Oscar, but suddenly Villa went on the attack through Benteke.
Chelsea's defence backed off the Belgian and he struck a low curling effort which almost skimmed the outside of the post.
Mourinho had seen enough of Torres and he replaced the Spaniard with Demba Ba while Andre Schurrle came on for Oscar.
The Chelsea manager's plans were then thrown into disarray when Willian earned a second yellow for pushing over El Ahmadi.
Mourinho disagreed with the decision, venting his fury towards fourth official Jon Moss.
The home crowd found their voice and urged Villa to push for a winner. Delph did well to gain a yard on Gary Cahill but he pulled his shot wide. Ron Vlaar was the next to miss, heading wide from close range.
Time was slipping away, but Villa found the goal they craved. Delph won the ball in midfield and fed a pass to Albrighton, who returned the ball to the former Leeds midfielder, who backheeled superbly past Cech.
Paul Lambert sprinted off the bench with his arms aloft in celebration.
Moments later he seemed to have a disagreement with Mourinho, but the two quickly made up.
Delph could have made it a perfect evening with a second but instead he struck the bar.
There was still time for more drama. Ramires was sent off for a lunging tackle on El Ahmadi. The Brazilian clashed with a furious Leandro Bacuna, who raced over to the midfielder and the pair jostled on the pitch.
More confrontation followed in the final minute of injury time as Mourinho marched on to the pitch to vent his fury at Foy.
The referee was having none of it and he ordered the Portuguese down the tunnel. After a minute of hesitation, the Chelsea boss walked off as play continued.
Villa repelled one last Chelsea attack and Foy blew his whistle, bringing an absorbing match to an end.