Rafa Benitez's side were given the chance to narrow Real's lead after the champions dropped points at home for only the second time this season.
Real were held to a 1-1 draw by Real Zaragoza on Saturday in a dress rehearsal for next week's King's Cup final.
Midfielder Francisco Rufete grabbed both Valencia goals, volleying in from 10 metres out after keeper Pablo Cavallero spilled a free kick five minutes before the break and then finishing off a rapid counter attack in injury time.
Earlier in-form Barcelona made the most of a slip-up by Deportivo Coruna to overtake the Galicians and climb to third place in the table with a 2-0 victory over basement club Murcia.
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Deportivo, meanwhile, look to have waved goodbye to their title chances following their 4-2 loss at struggling Real Mallorca.
Sunday's matches were preceded by a minute's silence in memory of the 200 victims of Thursday's train bombings in Madrid, with every player wearing a black armband.
CELTA SLUMP
The weekend's results mean that with 10 games left Real Madrid top the table on 61 points, four ahead of Valencia and nine ahead of Barcelona, while Deportivo are in fourth a further two points back.
Mallorca, who had not won in their last six outings, got off to a great start in the game of the day when the unmarked Fernando Correa smashed home a volley on seven minutes.
Depor managed to draw level when winger Pedro Munitis netted from close range but a headed goal from defender Ivan Ramis and a penalty from Cameroon striker Samuel Eto'o put the home side 3-1 up on the hour.
Deportivo substitute Djalminha pulled one back nine minutes from time, but Mallorca forward Jesus Parera put the result beyond doubt when he drilled under keeper Jose Molina after Eto'o had battled his way through the midfield.
Javier Irureta side's misery was compounded when defender Cesar was sent off for a second booking in injury time.
At the other end of the table, Murcia's defeat against Barcelona leaves them heading for a rapid return to the second division, while Espanyol's bid to escape from the drop zone suffered a setback when they lost 1-0 at home to Racing Santander.
Celta are also in serious trouble following their loss to Valencia. Radomir Antic's side are now five points adrift of Real Mallorca in 18th place in the 20-team division.