Los Che looked to have blown their chance to claim all the points after failing to build on the lead gifted to them by Mikel Balenziaga's first-half own-goal.
Henrique Sereno was handed a second yellow card for the foul that saw Valencia awarded a penalty in the 57th minute, but Roberto Soldado was unable to capitalise as his was spot-kick saved by the impressive Dani Hernandez.
Valladolid looked to have secured an unlikely point after Oscar Gonzalez lashed home a fine effort in the 71st minute, but with just 10 seconds left in added time Jonas rose to nod in Jonathan Viera's pinpoint cross to keep Valencia on the coat-tails of Real Sociedad.
Third-placed Atletico Madrid clung on for a goalless draw at mid-table Getafe despite ending a tetchy contest with nine men.
Both Mario Suarez and Diego Godin were dismissed for the visitors, who now trail city rivals Real Madrid by three points.
Espanyol took a giant step towards securing their top-flight future after beating Osasuna 2-0 at the Reyno de Navarra.
Hector Moreno gave the Catalans the lead early in the second half and Mubarak Wakaso made sure of all three points in stoppage time.
Rayo Vallecano picked up their first away win in just under three months after a 2-0 victory over Celta Vigo.
A smart finish by captain Piti gave the Madrid side the lead early in the first half and substitute Andrija Delibasic made sure of the points late on.
On Saturday, Barcelona, fuelled by Cesc Fabregas' hat-trick continued their relentless march to the title by crushing Real Mallorca 5-0, in a game that also saw Eric Abidal return to action for the first time since liver surgery.
Real Sociedad strengthened their grip on a top-four place with an impressive 4-2 win over UEFA Champions League quarter-finalists Malaga, while relegation-threatened Deportivo La Coruna picked up three vitals points after beating Real Zaragoza 3-2.
Meanwhile Real Betis's quest to qualify for Europe next season was given a massive boost as they thrashed a hapless Granada side 5-1 on Friday.
Friday's La Liga Result
Saturday's La Liga Results
Sunday's La Liga Results
Monday's La Liga Fixture