Liverpool were always in contention to the delight of manager Gerard Houllier following their worst spell for 18 years.
Villa, who were without their injured skipper, Steve Staunton, suffered a further setback during the delay before kick-off when Ronny Johnson dropped out of the side with a hamstring injury to be replaced by Mustapha Hadji.
It was the former Coventry City player's first start of the season.
Villa were far from outplayed at the start and Liverpool's defence was often at panic stations as indicated when Djimi Traore brought down Vassell for the penalty that was converted by the Villa striker.
Leonhardsen should have made amends but he wasted a fine opportunity after being set up by the industrious Gareth Barry.
Michael Owen was a handful but the versatile J Lloyd Samuel gave a masterly display to earn top marks for Villa.
But in the 54th minute Baros demonstrated his own class when he collected a John-Arne Riise pass and drilled home a low right-foot shot.
Baros set up Steven Gerrard for Liverpool's third goal in the 66th minute but Villa refused to lie down and Thomas Hitzlsperger pulled back a 72nd minute goal with another of his left-foot specials which whistled past Chris Kirkland.
It set up an explosive finish with Dion Dublin notching an 84th minute equaliser only for the industrious Murphy to complete a seven-goal thriller with Liverpool's winner following a pass from Gerrard.
Aston Villa: Enckelman, De la Cruz, Mellberg, Samuel, Barry, Hendrie, Hitzlsperger, Leonhardsen, Hadji, Vassell, Dublin. Subs: Postma, Allback, Angel, Kinsella, Edwards.
Liverpool: Kirkland, Babbel, Henchoz, Hyypia, Traore, Murphy, Gerrard, Diao, Riise, Owen, Baros. Subs: Dudek, Smicer, Heskey, Diouf, Carragher.
Referee: G Barber (Hertfordshire)