Jose Mourinho had never won at Villa Park heading into the fixture and Delph's well-taken goal after the break extended the Portuguese coach's misery in the Midlands.
To add insult to injury, Willian was sent off for a second bookable offence just minutes before the winning goal, while Mourinho would have been further incensed when Ramires saw red deep into injury time.
And the Chelsea boss then made matters worse for himself as he, too, was sent to the stands right at the death. There could have been a different outcome, meanwhile, had Nemanja Matic's effort on the stroke of half-time not been ruled out for handball.
|VIEW FROM VILLA PARK
|By Tom Davis at Villa Park
Drama here to end the second half at Villa Park as Ramires is dismissed for a challenge high over the top of the ball. It was unnecessary and caused confrontation on the pitch, including a red card for manager Jose Mourinho.
Chelsea found themselves frustrated all game after some terrific defensive play from Paul Lambert’s side but Willian’s red card swung the game, and momentum, in Villa’s favour.
It’s a massive blow for Mourinho, who is sure to lament decisions from the officials, who also ruled out Nemanja Matic’s goal for handball. It's a vital win for the home side as they take their tally to 34 points and another step towards safety.
And how will this result impact the title race?
Chelsea had Villa largely pinned back in their own half in the opening 10 minutes but the visitors were almost exposed by a Villa counterattack 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 through ball 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 save when El Ahmadi directed Hazard's cross towards his own 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.
And the hosts made the most of their numerical advantage when Marc Albrighton's cut-back from the byline went behind Delph - yet the midfielder somehow brilliantly 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. Mourinho then followed, after protesting the decision to give the Brazilian his marching orders.