The scoreline, however, hardly reflected the difference between the two teams as Blues battled bravely in their bid to move out of the bottom three.
Blues gave themselves hope with Chris Sutton's 226th-minute equalizer, but that faded in the second half.
Sutton's goal was something of a milestone as it was his 150th of his career and also Blues' 150th Premiership goal.
Unfortunately for Blues everything went against them.
Their tale of woe began even before the game started as Martin Upson, who has been out of action for several weeks with a pelvic strain, had to be assisted from the field in the warm-up session.
They then conceded an early goal through Baros and some four minutes later David Dunn, who has completed only two 90 minutes this season, limped out of the game.
As a result City were fighting a familiar battle trying to chase the game, and were rewarded by Sutton's equaliser.
Villa, on the other hand, were able to enjoy the luxury of an early lead and played with the confidence of a team moving out of trouble at the bottom of the table, only to be rocked back on their heels by Sutton's timely strike.
The two Midlands heavyweights have certainly not been punching their weight this season. If they could have shown the same commitment as on this occasion they would not have found themselves in such a precarious situation.
No one could say this vital game was boring in any aspect following an explosive start by both teams.
With so much at stake there was an obvious need to gain the upper hand as quickly as possible.
Villa achieved this objective with the crucial opening goal from Baros in the 10th minute.
It was a simple goal with Blues' defence exposed by the cross from Aaron Hughes, who had previously gained possession from James Milner.
The cross was deflected by Steven Davis to the unmarked Baros to score the easiest of his seven Premiership goals this season.
Milner popped up again two minutes later when he cleared a Martin Taylor effort off the line.
The departure of Dunn with a leg injury appeared to compound Blues' misery but the game had a long time to run.
Unlike in many games this season Birmingham were far from discouraged and conspired to take the game to Villa, and were rewarded for their attacking policy when Sutton grabbed an opportune 25th-minute equaliser.
The former Blackburn and Celtic striker had two attempts following a left wing cross from Kenny Cunningham and his second bid slipped low to the left of goalkeeper Thomas Sorensen.
Invariably Villa's attacks broke down against a determined Birmingham rearguard but early in the second half substitute Craig Gardner wasted a glorious chance to regain Villa's lead when he shot wide.
It was another Villa youngster, Cahill, who again set the game alight in the 56th minute when he hooked the ball home from close range following some determined work by Kevin Phillips.
Baros applied the killer blow in the 78th minute when he slotted home Villa's third goal following good work by Milner and Juan Pablo Angel.
The closing spell became a little over-heated with four bookings in the last six minutes.