Villarreal moved above Real Madrid and into the top four in La Liga after a 2-1 win over Levante on Saturday that piled more pressure on the struggling champions' coach Zinedine Zidane.
Valencia had two players sent off as they fell to a shock 2-1 defeat at lowly Las Palmas, while Atletico Madrid gave leaders Barcelona the chance to pull 11 points clear after only drawing 1-1 with Girona.
A 26th-minute penalty from Manu Trigueros and Real youth product Denis Cheryshev's first league goal in nearly two years saw Javier Calleja's side, who beat Real at the Santiago Bernabeu for the first time ever last week, move up to 34 points, two ahead of Real.
Zidane's team are fifth, level on 32 points with Sevilla, who crushed Espanyol 3-0 in a dominant display in Catalonia that gave Vincenzo Montella his first league win since arriving in Spain in late December.
The last time Real finished outside the top four was in 2000, when they placed fifth but won the Champions League -- a year before coach Zidane had even signed for the club as a player.
Madrid do have two games in hand on the teams around them, though, and host Deportivo on Sunday.
Cheryshev's tap-in, the first goal in La Liga for the injury-plagued attacker since March 2016, sealed the deal against Levante, who pulled one back with a stoppage-time penalty from Roger.
Russian international Cheryshev clattered into the post after charging down the left flank to tap home Enes Unal's low cross, but after some time on the ground in pain, struggled on until being substituted in the 65th minute.
"We are going to fight to finish as high as up as possible. Right now we are fourth but Madrid still have to play," said Calleja.
"We are ambitious. There is a long way to go but we are dreaming of doing the very best we can."
- Atletico and Valencia slip -
Antoine Griezmann's first goal in six league games wasn't enough for Atletico as they drew 1-1 with Girona and gave Barcelona a chance to extend their lead at the top.
The draw at the Wanda Metropolitano means Atletico are second and eight points behind Barca, who can almost end discussion over the league title with a win at Real Betis on Sunday.
Atletico stay second on 43 points, three points ahead of Valencia after their surprise defeat in a temperamental affair at Las Palmas, which saw defender Gabriel booked twice for dissent after giving away the host's winning penalty and then his centre-back partner Ruben Vezo sent off with three minutes left for elbowing spot-kick scorer Jonathan Calleri.
Valencia looked set for a routine win when Santi Mina headed home the opener from a corner after just five minutes, but Jonathan Viera smashed home Calleri's knock-down 15 minutes later.
Calleri slotted home the penalty that sealed the three points as Gabriel strode off to the showers.
Griezmann lashed home Diego Costa's brave knockdown for Atletico in the 34th minute but Portu snatched a shock equaliser for the away side 17 minutes from time.
Costa made his mark again on Saturday, with his second assist since returning from Chelsea adding to his three goals in five games in all competitions.
He lay down in a heap after being clattered by Girona goalkeeper Bono as he headed on for Griezmann, but it was the shot-stopper who came off worse and had to be substituted at half-time.