Real Sociedad produced a stunning fightback from 2-0 down to beat European champions Real Madrid 4-2 on Sunday.
Meanwhile, bitter rivals Barcelona made it two wins in as many games under Luis Enrique with a late winner at Villarreal.
Madrid were without the injured Cristiano Ronaldo and departed Angel di Maria and Xabi Alonso, but still looked on course for a comfortable evening when they flew into a 2-0 lead inside the opening 11 minutes thanks to goals from Sergio Ramos and Gareth Bale.
However, Inigo Martinez and David Zurutuza levelled for the hosts before the break and Zurutuza and Carlos Vela sealed a much-needed win for under-fire Sociedad boss Jagoba Arrasate.
Sociedad had lost their opening game at newly-promoted Eibar and been dumped out of the Europa League by Russian side FK Krasnodar in midweek and appeared down on their luck after another slow start.
Ramos rose highest to power home Toni Kroos' corner to open the scoring before Bale left Gorka Elustondo trailing with a neat nutmeg and slotted into the bottom corner.
Enaut Zubikarai then had to make fine saves to prevent Marcelo and Kroos putting Madrid out of sight.
But it was the hosts who crucially got the third goal as Martinez slammed home at the far post from Xabi Prieto's flick on.
Zurutuza then levelled four minutes before the break as he powered home Alberto de la Bella's pinpoint cross from the left.
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Iker Casillas produced a fine save to turn Imanol Agirretxe's header behind as Sociedad started the second period the stronger.
And they got their reward 25 minutes from time when Zuruztuza again timed his run into the box perfectly to connect with Prieto's low cross to the near post.
Madrid's humiliation was complete 10 minutes later when substitute Carlos Vela appeared to control the ball with his hand before spinning to fire into the top corner.
It was a happier evening for Barca as they were 1-0 victors at Villarreal thanks to 19-year-old Sandro Ramirez's debut goal eight minutes from time.
"It is gratifying to see the young guys score, but the most important thing is the victory," said Enrique.
"We kept going until the end. Villarreal defended very well and waited for the counter-attack to cause us problems.
"In the end we resolved things well and it reinforces what we have already seen in training."
Barca completely dominated possession in the opening 45 minutes, but failed to create clear-cut chances as Sergio Asenjo parried a drive from Pedro before turning a deflected Messi free-kick onto the post.
Villarreal's best opening of the first 45 minutes came when Victor Ruiz bundled the ball over the bar when completely unmarked at the back post.
However, they were nearly gifted the lead at the start of the second period as Barca defender Jeremy Mathieu turned Jaume Costa's cross off the outside of his own post.
Barca then upped the pace after Neymar replaced Munir El Haddadi and Asenjo had to be at his best again to turn away a well-struck Messi free-kick.
Ruiz then made amends for his miss in the first half with a miraculous block on the line to prevent Neymar smashing home Messi's low cross.
Yet, for all their chances, Barca were inches from being behind moments later when Tomas Pina struck the inside of the post and Javier Espinosa fired the rebound inches wide.
The visitors did finally make the breakthrough eight minutes from time when more fine footwork from Messi provoked another save from Asenjo, but Sandro was on hand to force the ball home from close range.
There was still time for a final scare for Barca as Giovanni dos Santos smashed a volley off the post from a narrow angle, but Enrique's men held on to go top of the embryonic La Liga table.