The inconsistent referee was blatantly at fault in awarding the dubious spot kick.
Darius Vassell lost possession in his run on goal and slithered into the back of Didier Domi before crashing to the ground.
Rennie immediately awarded the penalty which Angel dispatched for his 17th goal of the season but only after the unfortunate Domi had been booked by the controversial referee.
That one incident summed up Leeds' current plight as they eventually slumped to their sixth successive Premiership defeat as substitute Ronny Johnsen scored his first ever goal for Villa in the 59th minute.
Juan Pablo Angel, who is demanding fresh contract talks to keep him at Aston Villa, demonstrated his growing value with another goal to lift the Midlands club higher in the table.
Angel's 45th minute penalty was the crucial turning point of the game.
The last time Leeds picked up a point was on Boxing Day when they were involved in a draw at Elland Road against Villa but they had little chance of ending their harrowing run in the return game.
Unfortunately Leeds appear resigned to the inevitability of relegation to the First Division.
It was another impressive Villa win in what has been a roller-coaster season for the Midlands club.
The first home appearance of newcomer Nolberto Solano was well received by the home fans who were immediately impressed with the accurate crosses by the former Newcastle player.
Prior to the arrival of Solano no less than 90 per cent of Villa's goals had come from the left-hand side of their team.
Against Leicester all five came from the right and this balancing act was seen in good light against Leeds.
Solano has given Villa's front line that extra bit of class which could spark a good end of season run that could take Villa into contention for Europe.
Villa boss, David O'Leary, could have little satisfaction viewing the plight of his former club who are seemingly heading for relegation to cap their financial crisis.
But he was delighted with the outcome as Villa are now becoming a formidable force.
Afterwards O'Leary said: "It was a tough three points against a side who I cannot believe are where they are in the table.
"You look at the players on view, and if they continue to play with the same attitude, they have got to win games which will take them away from the relegation zone.
"I hope they do not go down as they are a big club and have enough players to get out of trouble. Let's hope they start winning games.
"I was pleased with the way we built on last week's win at Leicester.
"We got the goals at the right time although I thought from where I was standing the penalty was dubious to say the least.
"But I thought we should have had a penalty earlier in the game. We won the penalty, took it and we went in one goal up at half time.
"I was pleased that Angel wanted to get back into the action as quickly as possible. I cannot wait to get the link-up between him and Solano. They will prove invaluable for us.
"Angel's pre-match comments before the game were fair. I don't think that I will have to persuade him about anything.
"He knows how I think about him. He responds to me and like any good player he wants to be going places.
"Angel wants to be successful and I do as well."
Leeds manager, Eddie Gray, said: "I thought the boys worked extremely hard but it was a bad time just behalf half time to concede the penalty which I thought was harsh.
"But I still have a belief that we can scrape out of trouble. The lads were down at half time following the penalty because they had worked reasonably hard.
"I don't like looking at other results but other teams at the bottom of the table have also lost so Tuesday's game at Elland Road against Wolves is a big, big game for us.
"I just want us to win a game to give the lads a bit more confidence."
Following the 5-0 second-half hammering of Leicester City last week the big surprise was the return from injury of Angel in place of the obviously disappointed Peter Crouch following his two goals at The Walkers Stadium.
Leeds, to their credit, battled bravely but seemingly lacked a driving force in midfield despite some sterling work from Seth Johnson.
The Yorkshire club were sadly out of luck in the 17th minute. The promising James Milner was unlucky when his header clipped the crossbar from a Jermaine Pennant free kick.
Their failure to go ahead cost them dearly as they always appeared to be a little off the pace despite the industry of Mark Viduka.
Villa responded when Lee Hendrie turned and shot only to smash his effort against the crossbar.
Minutes later an out of touch Gareth Barry headed a Solano corner against the post.
The two players linked up again with Barry crossing from the left and Solano smashing his header against the bar as Leeds began to wilt.
Villa finally went ahead in the 45th minute with a penalty goal from Angel after Vassell won the spot kick when he lost possession and clattered into Didier Domi.
Domi, making only his second appearance of the season, was booked for complaining about the extremely harsh decision.
Villa finally sealed the fate of Leeds with a goal from substitute Johnsen in the 59th minute.
Only 11 minutes previously he had replaced replaced Dion Dublin. It was Johnsen's first ever goal for Villa and came with a header from another accurate cross from Solano.
Man of the match: Nolberto Solano - Made a good impression on his home debut with a series of tantalising crosses.