It was Angel's best performance in his three seasons in the Midlands and illustrated his growing confidence in a slowly improving Villa side.
Angel set the tone to Villa's success with an outstanding first-half strike and from then on Chelsea were always chasing the game.
Although Joe Cole grabbed a second-half equaliser it was Angel who created Villa's winner when his shot was blocked by goalkeeper Neil Sullivan only for the ever-alert Gavin McCann to hammer home a 78th minute winner.
In hindsight the seven changes made by Chelsea's manager, Claudio Ranieri, badly misfired as there was no great improvement from the side beaten by Bolton last Saturday.
This was emphasised in the 16th minute with Angel's spectacular goal which rocked Chelsea to their foundations and created an entirely different atmosphere.
Suddenly the whole tempo changed and it was sparked off by the running battle between the recalled Villa central defender, Ronny Johnsen, and Jimmy Hasselbaink.
Both players were spoken to by the referee but it appeared to make little difference.
Once Chelsea had settled down after the shock of going a goal behind they produced some sparking football. Cole wasted one good opportunity but he produced Chelsea's first shot on target just before the break which forced Thomas Sorensen to make a brilliant save diving to his left.
Glen Johnson was a driving force for Chelsea but Villa battled hard to retain their slender advantage with Johnsen and skipper Olof Mellberg the key to their first-half survival.
Ranieri's response to the situation was predictable in as much that he quickly sent on Frank Lampard, Hernan Crespo and Jesper Gronkjaer in an attempt to repair the damage.
Villa had to defend in depth as Chelsea built up several menacing attacks but it was the anxious Ranieri who breathed a sigh of relief when Angel's overhead kick went just wide.
Angel forced Sullivan to make another fine save to prevent a second goal from the Colombian striker in the 61st minute.
Crespo then wasted a great chance to equalise as he screwed the ball wide with only Sorensen to beat but in the 69th minute he set up the pass from which Cole equalised.
But Villa stormed back and Angel, who was always prepared to shoot on sight, hit another powerful drive which Sullivan parried into the path of the onrushing McCann to score his second winning goal in successive games.