In the day's only other Premier League game, former England striker Robbie Fowler improved his chances of gaining a permanent contract with Liverpool by clinching a 1-0 win at Blackburn Rovers.
Fowler, who rejoined Liverpool on a six-month loan from Manchester City in January, grabbed his fourth goal in his second spell with the club when he took a reverse pass from Fernando Morientes to side-foot home in the 29th minute.
Third-placed Liverpool have 73 points with three games left, three points behind Manchester United and 12 adrift of champions-elect Chelsea, 2-0 winners at Bolton on Saturday. Blackburn, chasing a spot in next season's UEFA Cup, remained sixth on 54 points.
Villa, who also beat Steve Bruce's side earlier this season, secured their first Premier League double over their neighbours to leave third from bottom Birmingham firmly anchored in the drop zone.
Birmingham, who have 29 points from 34 games, are three behind Portsmouth with four matches remaining. The bottom three go down.
"We are still in there with a chance but we needed to beat Villa to keep the pressure on Portsmouth," Bruce told reporters. "We live to fight another day and we'll give it everything we can."
GOOD START
Villa made a good start when the unmarked Baros pounced on a 10th-minute cross from Aaron Hughes to fire the ball past goalkeeper Maik Taylor from eight metres.
Birmingham, who had not lost in the league at Villa Park since 1983, equalised 15 minutes later when Emile Heskey nodded the ball on for Chris Sutton to drive the ball low into the net with his left-foot from 12 metres.
Villa regained the lead in the 56th minute, 20-year-old defender Gary Cahill grabbing his first goal in his third league appearance with a spectacular overhead kick.
David O'Leary's men had gone six games without a victory but Baros banished lingering relegation fears for 15th-placed Villa when he finished a neat move with a venomous right-foot shot with 12 minutes left.
After his goal at Blackburn secured Liverpool's sixth win in a row, Fowler said he had no idea whether manager Rafael Benitez would be offering him a new contract at the end of the season.
"I am as much in the dark as everyone else," said Fowler.
Benitez made it clear he had yet to make up his mind although he said his decision would be made easier if Fowler continued scoring goals.