Following the home defeats to Barcelona and Ajax that ended their hopes of major honours this season, Madrid had already benefitted from a missed penalty and two disallowed Valladolid goals at the Jose Zorrilla before Anuar gave the hosts a 29th-minute lead.
But Raphael Varane was gifted an equaliser and Karim Benzema headed Los Blancos into a two-goal lead in the 59th minute, having dispatched a spot-kick eight minutes earlier.
Casemiro was sent off nine minutes from time for third-place Madrid, although Ballon d'Or winner Luka Modric slotted in a fine fourth – taking attention away from speculation Jose Mourinho could replace Solari in the coming days, at least temporarily.
The soon-to-be deposed European champions did their under-fire coach no favours whatsoever with a display of comical ineptitude during the opening half an hour.
Alvaro Odriozola hauled Oscar Plano over to concede a penalty that Ruben Alcaraz promptly put into orbit.
Sergi Guardiola was more precise in front of goal, only to see two efforts in quick succession ruled out for offside, but Madrid continued to be cut open at will.
Anuar found the breakthrough from close range after Guardiola diverted Keko's searching ball back across goal, although Valladolid's lead was short-lived.
Fittingly, Madrid's equaliser came with a dose of slapstick as Jordi Masip missed his punch from a corner and Varane prodded in.
Antonito and Anuar went close before Odriozola burst into the Valladolid box to draw a clumsy foul from Plano and Benzema coolly converted.
Masip brilliantly kept out Dani Ceballos' 57th-minute volley, only for Benzema to capitalise on more slack set-piece defending by powering home Toni Kroos' corner.
Guardiola wrapped up a luckless outing by volleying against the base of the post and Casemiro needlessly earning a second booking by blocking a quick free-kick showed unease that was only settled when Modric skipped past Joaquin Fernandez to finish.
What does it mean? Solari's days remain numbered
Solari is not responsible for the problems that leave Madrid at their low ebb, but neither has he done enough to alleviate them. The wretched nature of their first-half showing could and should have been more heavily punished. Victory might have followed, but Solari is not the man to turn this ship around.
Benzema leads by example
With Sergio Ramos still absent, Benzema took the captain's armband. A player who has at times suffered merciless criticism from sections of the Madrid support, he has proved a reliable presence in a chaotic season. He led the line diligently as things threatened to dissolve behind him before the break and he brought an air of authority to the pivotal penalty that Alcaraz badly lacked.
Ailing Asensio's stalled progress
Benzema is 31, however, and unlikely to remain part of Madrid's plans much further into the post-Cristiano Ronaldo era. That burden falls on the likes of Marco Asensio. But aside from his wonderful lofted pass for Ceballos' second-half chance, the richly gifted attacker loitered on the periphery in a display emblematic of a season where his progress has stalled.
Madrid are at home next weekend against Celta Vigo, who sit in a relegation zone Valladolid remain a point above. Sergio Gonzalez's men will look to ease their plight when they travel to Eibar.