Real Madrid needed a stoppage time winner from Brazilian midfielder Casemiro to move back within 12 points of La Liga leaders Barcelona with an unconvincing 2-1 win at Las Palmas.
Sergio Ramos's towering first-half header put the visitors in front, but Las Palmas looked to have salvaged the point their performance deserved through Willian Jose three minutes from time yesterday.
However, Casemiro punished some atrocious marking to head home the winner before Ramos was sent-off for the 20th time in his Madrid career late on.
More From This Section
And Sevilla maintained their hopes of Champions League football next season with a thrilling 4-2 win over Villarreal.
Madrid goalkeeper Keylor Navas had been on top form as Real saw off Roma to reach the Champions League quarter-finals in midweek and was consistently called upon to save his side in the Canary Islands.
"I go away happy with the result, but a little worried with what I saw in the second-half," said Madrid boss Zinedine Zidane.
"If we want to aspire to something in the future, we have to play better. That is clear because playing like this we won't go anywhere."
A rare misplaced pass from Luka Modric released Jose in behind the Madrid defence early on, but Navas raced from his line to block.
Cristiano Ronaldo then fluffed his best chance to increase his lead over Luis Suarez in the fight to be La Liga's top scorer as he fired too close to Javi Varas.
However, Madrid did take the lead from the resulting corner as Ramos rose highest to head home Isco's delivery.
Las Palmas had by far the better chances after the break to extend their recent unbeaten run to four games.
Yet, a mixture of poor finishing and defending cost them as Momo and Nili saw their efforts smothered by Navas before Sergio Araujo headed over from point-blank range.
Jose looked to have finally earned the hosts a point when he dinked Momo's pass over Navas three minutes from time.
But Madrid retook the lead as the game entered stoppage time when Casemiro was left unmarked to head in Jese Rodriguez's corner at the back post.
And there was still time for Ramos to see red for the first time in two years for a second bookable offence.
- 'Indefensible performance' -
==============================
Earlier, former Manchester United striker Giuseppe Rossi's solitary goal revitalised Levante's chances of beating relegation as they moved to within three points of safety despite remaining bottom of the table.
Neville has now won just three of 15 La Liga games in charge with Valencia rooted in mid-table mediocrity in 12th, just eight points above the relegation zone.
"I take responsibility for the defeat, but that was an indefensible performance, unacceptable and not good enough," said Neville.
"I apologise to the fans of Valencia because the very basic premise of a football match is that you run, fight and tackle as hard as the opposition."
Valencia's season now hinges upon overturning a 1-0 first-leg deficit at home to Athletic Bilbao in the Europa League on Thursday.
Neville insisted before the game that he will fulfil his duties as an England coach during a 10-day international break later this month.
That decision is likely to come under further scrutiny in the coming week with his future at the Mestalla far from secure.
At the other end of the table, Sevilla moved to within five points of Villarreal in fourth as they came from behind to register a 16th straight win at home.
Vicente Iborra finished off a brilliant counter-attack to give Seville the lead.
However, Cedric Bakambu continued his fine form with a double to give Villarreal a 2-1 half-time lead.
Victor Ruiz's own goal restored parity for the hosts before Yehven Konoplyanka's stunning long-range strike regained the lead and Jose Antonio Reyes rounded off the scoring in stoppage time.
Athletic Bilbao also moved to within six points of Villarreal with a convincing 3-1 win over Real Betis.