Angel's opening two goals put Villa on the winning path and at the same time sent Wolves deeper into trouble and anchored them at the foot of the table.
It was Villa's 42nd success in the 97 games between the two Midlands clubs and the fifth successive time Wolves have failed to beat their Birmingham neighbours in this local derby.
Villa's commitment to attack was emphasised by the decision of manager David O'Leary to include his three international strikers.
It was a ploy which paid off almost immediately with Angel capitalising upon a shell-shocked Wolves defence which had conceded ten goals in their previous two games.
Angel was twice on the mark in a two-minute spell but Wolves commendably hit back with a goal from Alex Rae to put the game into the melting pot.
Gareth Barry scored Villa's third in the 48th minute but Wolves refused to concede defeat and kept in contention with a Mark Kennedy goal ten minutes from time.
Despite never being in arrears Villa made hard work of their success particularly in the last 20 minutes when Wolves were the more positive in their quest for a point.
Villa had an early scare when Colin Cameron missed an early opportunity when he blazed his shot wildly over the bar.
A suspect Wolves defence was punished in the 21st minute when Angel turned a low cross from Barry past Michael Oakes.
Angel was again on the mark two minutes later when Mark Delaney left Paul Butler in his wake before pulling the ball back into the path of Angel to slide home his tenth goal of the season.
But then Villa sat back and paid the penalty when a pass from Cameron bounced off Barry into the path of live-wire Rae to fire in his fourth Premiership goal of the season.
Three minutes into the second half another Delaney cross was finished off by Barry for his first goal since the opening day of the season at Portsmouth.
Yet again Villa sat back and with Olof Mellberg stranded in the other half of the pitch Kennedy ran on to a Kenny Miller pass in the 80th minute to leave Villa hanging on grimly for their vital win.