The former Arsenal forward struck midway through the first half with a smart finish, punishing the visitors for having more of the ball but failing to create chances.
Martinez's side got more sights of goal in the second half but were unable to take advantage, slumping to a second consecutive defeat that keeps them second bottom of the Primera Division.
Jagoba Arrasate's side meanwhile stay sixth in the table, cutting the gap between themselves and Athletic Bilbao in fourth to seven points.
La Real could have taken the lead within the first minute, Antoine Griezmann finding a gap to shoot into but the Valladolid goalkeeper Jaime saved comfortably.
Haris Seferovic was presented with a far better opportunity just before the quarter hour mark, arriving in the six yard box to finish off a pass from Joseba Zaldua, but was denied by Jaime.
A goal for the hosts was beginning to look likely and duly arrived in the 23rd minute, Vela chesting down a lofted pass from Ruben Pardo and then firing past Jaime.
La Real could have extended their lead on a couple of occasions before half-time. First Sergio Canales' shot shaved the post; then Vela burst forward on the break to shoot at Jaime, who repelled the effort, Seferovic sending the rebound over the bar.
The best chance for the visitors in the opening 45 minutes fell to Javi Guerra, but the club's top scorer was unable to keep his shot below the crossbar.
Dani Larsson played in Oscar Gonzalez early in the second half, the forward left with just Claudio Bravo to beat, but the Chilean goalkeeper made himself big to deny Oscar.
Valladolid's best chance of the game arrived just after the hour mark, Stefan Mitrovic heading the ball towards Oscar inside the six yard box, but the forward volleyed over the bar, squandering the second of two golden chances in the space of four minutes.
With 12 minutes remaining Valladolid won a free-kick that would have been prime territory for former winger Patrick Ebert, but was too far out for Victor Perez to cause any concern for Bravo, and the troubled team's hopes of getting anything from the game vanished as the ball trickled wide of the post.