Arsenal were relieved when Anderson's free-kick was half-cleared and Michael Carrick turned the loose ball wide.
Hernandez struck first, looping a header over Petr Cech from Michael Carrick's floated pass.
But after Michael Carrick handled in the area, Ballack won it from the spot.
Michael Carrick was absolutely magnificent playing in front of the back four - but Wayne Rooney was the story.
Webb later sent off Steven Gerrard in the 32nd minute for a challenge on Michael Carrick.
Ryan Giggs and Michael Carrick also had efforts from range to keep home keeper Petr Cech interested.
United struggled overall but got a consolation goal when Michael Carrick shot into the corner in injury time.
United also had defender Nemanja Vidic sent off for two yellow cards and lost Michael Carrick to injury.
Eriksson instead decided to take all three of Michael Carrick, Jermaine Jenas and Owen Hargreaves - a nonsensical move.
BBC: SPORT | Football | World Cup 2006 | Teams | England | Eriksson exposed by his Owen goal
Michael Carrick's drive hit Richard Hughes and thumped in off the bar and Dimitar Berbatov's shot made it 4-0.
Wayne Rooney got the ball rolling with a clipped finish from Rafael da Silva's cross, before Michael Carrick swept in.
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The Cameroon international cut inside to elude the challenge of Nemanja Vidic before toe-poking the ball home as Michael Carrick vainly challenged.
Great teams have all-rounders in that role, guys who are also skillful passers, like Manchester United's Michael Carrick or Barcelona's Sergio Busquets.
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The Portuguese winger smashed home a trademark free-kick from 25 yards before turning provider for Michael Carrick to fire in United's second.
Midfielder's Michael Carrick and Darren Fletcher started at the back with full-back Patrice Evra, and were put under heavy pressure early on.
Frank Lampard was also missed in central midfield, where the starting partnership of James Milner and the very disappointing Michael Carrick failed to fire.
Tottenham boss Harry Redknapp called for match officials to use technology which might have overturned Webb's decision that Heurelho Gomes had fouled Michael Carrick.
Ferguson made a triple substitution in the 61st minute, sending on Owen Hargreaves, Anderson and John O'Shea for Patrice Evra, Michael Carrick and Ferdinand.
Arsenal failed to clear a corner, and when Michael Carrick's cross was deflected into his path by Mikael Silvestre, O'Shea lashed a finish high past Almunia.
Defoe went first for Spurs and scored, Stephane Henchoz stepped up for Liverpool and scored and then Michael Carrick and Richie Partridge made it two apiece.
BBC: SPORT | Football | League Cup | Tottenham 1-1 Liverpool
And United posed the first danger after the break when Friedel saved well from Michael Carrick, whose shooting had been very erratic up to that point.
Ferguson has already revealed his intention to play midfielder Michael Carrick in central defence while another midfielder, Darren Fletcher, seems certain to occupy a defensive berth too.
He joins his club team-mate Jermain Defoe on the standby list, while Paul Robinson, Michael Carrick, Jermaine Jenas and Aaron Lennon were named in the 23-man squad.
BBC: SPORT | Football | World Cup 2006 | Teams | England | Dawson gets England standby call
Wayne Rooney equalised after a mistake by Ricardo Carvalho but Ballack struck the winner from the penalty spot after 86 minutes following a handball by Michael Carrick.
As well as taking goal celebrations into account, the officials were entitled to add 30 seconds for United's stoppage-time substitution, when Michael Carrick come on for Anderson.
Capello's heavily-disrupted plans were subjected to even further alteration late on when Michael Carrick suffered an ankle injury - allowing Jermaine Jenas to make a rare England start.
United wasted a glorious chance when Michael Carrick hooked over the Villa defence for Rooney, who found himself clean through but fired horribly high and wide from close range.
Ferguson was thought to be upset that Dean, having already booked Michael Turner, did not send the Hull defender off when he up-ended Michael Carrick in the second half.
United boss Alex Ferguson had been forced to pair England midfielder Michael Carrick with left-back Patrice Evra in the center of defense after Neville and Brown went off injured.
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