Sevilla scored an even more emphatic victory in the night's other quarter-final first leg, as they cruised to a 4-0 win at home to a weakened Atletico Madrid side.
Goals from Raul, Ronaldo and Luis Figo had already put Real in charge of the heavyweight clash at the Bernabeu when Beckham picked up a second booking in the 87th minute for a challenge from behind on Pablo Aimar.
League leaders Valencia made a dazzling start against their chief rivals for the league title, fizzing passes in front of the Real defence and twice going close in the opening few minutes.
Albelda looked odds on to score when he controlled the ball inside the box but the Spanish international midfielder's shot drifted just wide.
Mista then wasted a clear
Real took the lead when Raul met a Santiago Solari cross with a glancing header in the 32nd minute.
Valencia pressed for an equaliser in the second half but Ronaldo blasted in Real's second in the 81st minute and Luis Figo made it 3-0 from the penalty spot after Carlos Marchena had brought down Raul.
Two minutes later Beckham was sent off for the first time since joining the Spanish champions and was given a rousing ovation as he left the field.
He was swiftly followed by Valencia midfielder David Albelda, who was also booked for a second time in a separate incident.
Three goals in 10 minutes midway through the first half set Sevilla on their way, with a Julio Baptista free kick rounding off victory in the 73rd minute.
In the remaining two ties on Thursday, Alaves, the only second division side left in the competition, host Celta Vigo, while Barcelona are at home to Real Zaragoza.