Vinicius Junior came off the bench to force an own goal off Kiko Olivas in the 83rd minute before Sergio Ramos ensured the European champions finished a poor showing on an upbeat note with a penalty five minutes later.
Valladolid had rattled the crossbar twice in the second half and will count itself highly unfortunate not to have further opened the wounds inflicted during last weekend's El Clasico humiliation.
Solari, who replaced the sacked Julen Lopetegui following that 5-1 loss, presided over a 4-0 Copa del Rey victory over third-tier Melilla in the first match of his caretaker stewardship, but for the first 80 minutes this was a sobering reminder of the work needed to mend a misfiring side.
Marcelo's absence afforded Sergio Reguilon a LaLiga debut and the left-back, the target of Ramos' fury during a training ground incident last month, created early opportunities that Karim Benzema and Gareth Bale both wasted.
The malaise eventually spread to the other end as only wasteful finishing from Antonito and Enes Unal prevented the home fans' whistles from growing louder.
Valladolid looked the more likely to break the deadlock after the interval with Thibaut Courtois' crossbar denying both Ruben Alcaraz and Toni Villa.
But it was to be a cruel end for the impressive visitor as Vinicius' heavily deflected shot left Jordi Masip with no chance, before Fernando Calero's sloppy foul on Benzema allowed Ramos to snap his side's five-game winless run in LaLiga, moving it temporarily to within four points of leader Barcelona.