Soldado leads Valencia over Sevilla
Valencia made it seven wins from eight games under Valverde to move up to seventh in the Primera Division, a point behind Malaga in the final Champions League spot in fourth. Sevilla remain 12th in the table following the loss.
Sevilla had the first opening in the ninth minute but Ivan Rakitic fluffed the chance from inside the area.
Valencia's Ricardo Costa forced the ball over the bar after 11 minutes when Pablo Piatti's corner found him unmarked running in at the far post, the ball hitting his leg before going over.
Sevilla hit straight back but as Jesus Navas cut in from the right he fired in a shot which Diego Alves got down to save.
Alvaro Negredo was poised to have an effort from close range after Rakitic's cross was deflected towards him but the home defence cleared.
Valencia continued to press in search of the opening goal but despite Piatti's delivery from set-pieces the home side were unable to find an opening goal.
Sevilla were defending in numbers as they frustrated Valencia who were unable to add the finishing touch to their good approach work.
In a rare Sevilla foray into the Valencia half Negredo cut in from the right and crossed the ball with his left foot but it failed to find Jose Antonio Reyes and the home defense cleared the danger.
Emir Spahic was booked after 38 minutes when he pushed over Ever Banega outside the Sevilla area but substitute Tino Costa, on for David Albelda, fired the free-kick over the bar with his first meaningful contribution.
Fernando Navarro was booked in the opening minutes of the second half for a foul on Piatti but Tino Costa wasted the free-kick with an over-hit delivery.
Valencia broke the deadlock five minutes into the second half when Adil Rami headed Piatti's corner towards goal and an unmarked Soldado forced the ball home from close range for his 10th goal in La Liga this season.
There were chances at both ends before Rami's foul on Negredo presented Sevilla with a free-kick which Reyes floated into the box but the home side cleared.
Rakitic fired in another free-kick which Valencia had to work hard to eventually clear.
Valencia cleared from another free-kick and broke clear but when Joao Pereira passed to Ricardo Costa he shot straight at a defender.
The home side relieved the pressure but Tino Costa wasted a chance when he fired well over from outside the area.
Reyes broke clear down the left but his low cross was straight to a defender as Sevilla continued to look for an equaliser.
Gary Medel conceded a free-kick to the right of the Sevilla area when he fouled Andres Guardado but the set-piece was easy for Rakitic to clear at the near post.
Rakitic floated over a free-kick into the Valencia area but Spahic was offside when he headed the ball wide.
Nelson Valdes and fellow substitute Tino Costa both wasted openings before Rakitic set up substitute Miroslav Stevanovic but his shot was saved by Diego Alves.
Soldado rounded goalkeeper Diego Lopez but Medel cleared in front of his own goal but Soldado was not to be denied an 11th league goal of the season with a header from Banega's corner with two minutes to go.