Real Madrid needed a last-gasp penalty to beat Elche on Wednesday, while Sevilla sealed their first win of the season over Rayo Vallecano.
Cristiano Ronaldo had put Carlo Ancelotti's side ahead in the 51st minute at the Estadio Manuel Martinez Valero.
But in an exhilarating finish Richmond Boakye looked like he had secured a point for Fran Escriba's charges when he levelled proceedings in the 91st minute.
The drama was not finished there, however, as Real were handed a controversial penalty when Pepe was adjudged to have been hauled down by Carlos Sanchez in the area.
Ronaldo duly stepped up to despatch the spot-kick in sixth minute of additional time, as Real maintained their unbeaten start to the campaign, and sit two points adrift of Barcelona and Atletico Madrid in third.
There was also late drama at the Estadio Nuevo Los Carmenes as Granada were cruelly denied a point in a 1-0 loss at home to Valencia.
With the match looking certain for a 0-0 stalemate, Jonas snatched the three points in the fourth minute of extra time.
It secures back-to-back victories for Miroslav Djukic, to ease the pressure that had mounted after a slow start to the season.
Sevilla routed Rayo Vallecano 4-1 at the Estadio Ramon Sanchez Pizjuan, to earn their first Liga victory of the campaign.
Ivan Rakitic scored from the penalty spot 17 minutes in before adding another goal in the second half to give Sevilla a two-goal cushion.
Adrian halved the deficit in the 55th minute, but a brace in the last 10 minutes from Carols Bacca completed the comfortable win for Sevilla.
|24||C. Sánchez||90+5' 90+8'|
|14||Manu del Moral||7'|
|Coach: Fran Escribá|
for Manu del Moral 59'
for Javi Márquez 62'
for Coro 81'
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