Valverde stunner saves Real Madrid title hopes against Bilbao
Madrid stayed four points behind Barca after Valverde smashed into the top corner with a sliced, swerving effort.
After Champions League elimination by Arsenal it looked like Madrid were set for another devastating result until the Uruguay international's stoppage-time intervention.
"Fede has such a good shot... in training yesterday he shot a ball that looked like it was going out and then it picked up a curl like that and you go 'how do you shoot like that?'" said Madrid goalkeeper Thibaut Courtois.
"In training he does that once or twice a week."
Athletic Bilbao, who reached the Europa League semi-finals on Thursday by beating Rangers, rotated heavily.
Despite that, the Basque side proved a hard nut for Madrid to crack, especially with their top goalscorer Kylian Mbappe both suspended and recovering from an ankle problem.
The forward was whistled by some fans for his failure to help the team overcome Arsenal in the Champions League quarter-finals in midweek when he was shown watching the game on the stadium screens.
"Valverde was key in this game because he scored the goal," said Real Madrid coach Carlo Ancelotti.
"The team was good, a bit slower in the first half but very good in the second.
"We wanted to win, we wanted to react after the elimination against Arsenal -- the team came through and Fede was the key player."
Vinicius, who was previously criticised by Ancelotti for lack of defensive work ethic, was running hard on the left, which fans at the Santiago Bernabeu appreciated.
The Brazilian has struggled for form at times this season but was Madrid's brightest player against Athletic, giving Unai Nunez a difficult night.
Madrid played with intensity after their European elimination, trying to keep La Liga in their sights after Barcelona made a late comeback to beat Celta Vigo on Saturday.
Rodrygo Goes came close early in the second half before Athletic goalkeeper Unai Simon saved from Eduardo Camavinga.
The hosts began to push Athletic deeper and started to create better chances.
Madrid turn screw
Vinicius bent a delicious cross with the outside of his boot into the six yard box for Jude Bellingham to meet, but Simon made an excellent save to tip over his header.
Fede Valverde fired narrowly wide of the near post and Vinicius did find the net but Endrick was offside in the build-up.
Bellingham appealed for a penalty after going down softly in the area and then fired over from close range in the final stages.
It was the kind of chance the England international managed to turn into late match-winning goals last season as he inspired Madrid to La Liga and Champions League glory.
Instead it was Valverde who took up that role with his sublime blast which left Simon with no chance.
"Valverde has an extraordinary shot," said Athletic coach Ernesto Valverde.
"We had a really good game (but) they are individually very good, Vinicius was very good."
Madrid's victory offers them hope of salvaging their season and a morale boost ahead of next weekend's Copa del Rey final against Barcelona.