Guedes picked the ball up in his own half and surged past four Osasuna players before completing his stunning run with a driven shot into the top corner.
Rodrigo Moreno made it two at Mestalla and while Osasuna had chances in the second half, Valencia secured a comfortable win to keep their fading hopes alive of finishing in the top four. Valencia stay eighth but reduce the gap behind Sevilla in the last Champions League spot to six points.
Osasuna, who were expected to be among the teams most affected by empty stadiums given their passionate local support, drop to 12th. They have now taken just one point from their three matches since the restart, this defeat coming on the back of a 5-0 loss at home to Atletico Madrid.
Games against Alaves, Leganes and Eibar - opponents all currently beneath them in the table - should decide whether they get dragged into a relegation scrap during the run-in. Osasuna might wonder how Guedes managed to carry the ball through two thirds of the pitch without being stopped but the Portuguese should take full credit for what is surely a contender for goal of the season.
After a superb first year on loan from Paris Saint-Germain, Valencia paid 40 million euros to sign Guedes permanently in 2018 but the 23-year-old has struggled to deliver on his early promise. Yet this was a timely reminder of what his talent, a fabulous goal coming before a pin-point pass that allowed Rodrigo to make it two.
Guedes' moment came after he intercepted Inigo Perez's cross-field ball and began driving forward. He advanced over the half-way line before slaloming around Oier, tumbling past Unai Garcia but getting up quick to nick the ball ahead of Raul Navas. Into the penalty area, Guedes finally cut inside David Garcia before dummying a shot and then curling into the net. Guedes turned provider soon after, collecting a poor pass from David Garcia and setting free Rodrigo, who prodded home his second goal in three games.
Osasuna's next opponents will be Alaves, who earlier suffered a crushing 6-0 defeat away at fellow strugglers Celta Vigo. Alaves were reduced to 10 men after 27 minutes when Martin Aguirregabiria was sent off and Celta capitalised, scoring four in the first half and adding two more late on.