The 27-year-old midfielder rose to head home from Manuel Lolo's fine cross after 84 minutes following many missed chances from the home side at Jose Zorrilla.
Javi Gracia's Osasuna had recorded three defeats in their last four matches before Friday night's game and their win moves them out of the relegation zone and into 15th position in La Liga, while Valladolid drop a place to 16th ahead of Saturday's action.
The home side started well and had their first shot on target in the opening minute as Daniel Larsson fired the ball into the danger zone from the left, just outside the box, forcing Osasuna goalkeeper Andres Fernandez to make a save.
It took both sides a few minutes to settle into the match before Javier Guerra Rodriguez had a weak shot on target for Valladolid, followed up with another from Miguel De las Cuevas which sailed over the crossbar.
Zakarya Bergdich was next to test the visiting defence but Jordan Loties was quick to put in a block, while it took Osasuna until midway through the first half before they had a chance to take the lead.
Alvaro Cejudo could have put Los Rojillos ahead with a great chance from just outside the box after 27 minutes, but Valladolid stopper Diego Marino's safe hands were quick to keep the ball out and deny them.
Juan Ignacio Martinez's men continued to push forward and could have gone in front 10 minutes before the break, however Fernandez was well placed to catch Patrick Ebert's long-range effort.
Both sides took a while to get going in the second period and it was not until just before the hour mark that either team came anywhere close to breaking the deadlock.
Alvaro Rubio attempted to put the home side ahead, but his drilled effort from the right just missed the target as the ball floated past the post.
But the away side were not giving up and De las Cuevas was next to have a shot at goal before he too fired just wide as Osasuna began to come back in the game.
And after 84 minutes, their second-half pressure paid off as they took the lead.
Defender Lolo collected the ball and set up Oier from the left wing, who made no mistake with his head as he netted a close-range winner for the visitors.