The midfielder showed a brilliant piece of ingenuity in the 82nd minute to turn home substitute Marc Albrighton's centre and hand Paul Lambert's side all three points at Villa Park.
Jose Mourinho had stated that Manchester City were favourites to lift the Premier League crown during the week, and there was an element of truth to the Chelsea manager's words as his side failed to break down a resolute Villa defence.
There could have been a different outcome had Nemanja Matic's effort on the stroke of half-time not been ruled out for handball.
But Chelsea's indiscipline ultimately cost them - Willian was shown a red card for a second bookable offence in the 68th minute before Ramires was also dismissed in injury time following a crude challenge on Karim El Ahmadi.
Chelsea still retain a six-point lead over second-placed City, though Manuel Pellegrini's men have three games in hand to cut the gap, while Villa's win lifts them to 10th.
Chelsea had Villa largely pinned back in their own half in the opening 10 minutes, but the visitors were almost exposed by a Villa counter-attack that ended with Christian Benteke heading Delph's cross wide.
Mourinho's men were comfortable in possession, however, with Oscar looking particularly lively - the Brazilian curling a shot just wide after 15 minutes as he ventured forward.
After a promising opening, the game suffered something of a lull, but it was Chelsea who continued to look the more likely to score and Fernando Torres fired wide from a tight angle after a neat throughball from Eden Hazard after 35 minutes.
Villa's biggest threat was on the counter, and the lively Benteke saw an acrobatic half-volley from the right-hand side of the box fly wide of the far post.
The home side then had a huge let off five minutes before the break. Willian's corner was flicked to the back post by John Terry, where Matic squeezed the ball home - only for referee Chris Foy to rule the goal out for a handball by the Serbia international.
Chelsea continued to dictate the tempo after the break, and Villa goalkeeper Brad Guzan had to make a smart reaction stop when El Ahmadi directed Hazard's cross towards goal when sliding to make a block.
The second half followed a similar pattern to the first, with Chelsea continuing to probe but failing to find a way through a stern Villa rearguard.
Villa retained a foothold in the game, and Benteke should have done better when he received a pass from Andreas Weimann on the edge of the area and placed a shot narrowly wide of Petr Cech's goal.
With just over 20 minutes remaining Chelsea were reduced to 10 men. Willian - who had already been booked in the first half - was rash in pulling back Delph and was shown a second yellow card, although the decision was perhaps harsh on the Brazilian.
The hosts made the most of their numerical advantage when Albrighton's cut-back from the byline went behind Delph, but the midfielder somehow flicked home.
Delph then went close to a second when his shot was deflected onto the crossbar by Terry, before Chelsea's match ended in further ill-discipline when Ramires was sent off for a lunging tackle on El Ahmadi.
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