Real had been fortunate not to go behind on two occasions in the second half when Ruben Alcaraz and Toni Villa hammered the crossbar, but the home side sealed a first win in six league games when captain Sergio Ramos netted an 88th-minute penalty.
Maybe it's the way that someone can read into it, but the 28-year-old German doesn't seem to be overwhelmed at the fact that Madrid have picked up their first league win since a 1-0 victory over Espanyol in September.
Madrid have moved up to sixth place and are on 17 points, though La Liga leaders Barcelona are seven points clear of their rivals.
Mac Miller's death confirmed as 'accidental overdose'
A person close to Miller, whose real name was Malcolm James McCormick, said he had spent the evening watching football. The night before his death, Miller was reportedly casually hanging out with friends and was watching football.
Solari is now the interim manager at the Bernabeu after the sacking of Julen Lopetegui following their 5-1 humbling in last week's El Clasico. We understand how the fans feel. We have to change that, and after we scored the fans were lifted again. "With more results, we will get back the confidence of the fans in a team which has won a lot".
Not even usual favourite Marco Asensio escaped the howls of unhappy supporters when he made way for Vinicius, who had barely played under Solari's predecessor Julen Lopetegui.
The former Real Madrid player didn't have long to get comfortable before taking his side to Segunda Division side Melilla on Wednesday in the Copa del Rey.
Real Valladolid then caused hearts to skip beats as they rattled Thibaut Courtois' woodwork, before Vinicius came on and changed the game as he forced an own goal. I think they will stick with Santiago Solari until they can see a way of getting Pochettino.
"I would like to win every game 7-0 with three bicycle kick goals but football is more complicated than that".