The defeat leaves Madrid just a single point clear of Barcelona and three points ahead of Sevilla.
The defeat leaves Madrid just a single point clear of Barcelona and three points ahead of Sevilla and now enjoy just one game in hand over their title rivals.
"We lost this match in the opening ten minutes, ten bad minutes where we let two goals in," Eeal coach Zinedine zidane told Spanish TV.
"I'm not worried, I'm angry more than anything, because we only have ourselves to blame."
Italian striker Zaza had broken down in tears after scoring his first goal since May at the weekend, but showed his confidence is suddenly sky high with a brilliant volleyed finish to open the scoring on five minutes.
Orellana then finished off a flowing counter-attack on nine, but Cristiano Ronaldo halved Madrid's arrears with a towering header from Marcelo's cross a minute before half-time.
Madrid boss Zidane introduced Gareth Bale off the bench on just his second appearance after a three-month injury layoff for the final half hour.
And the Welshman nearly rescued a point when his header from point-blank range was blocked by Enzo Perez a minute from time.
Madrid's Brazilian wing-back Marcelo agreed with his coach that they had thrown the game away early.
"We're still top but we really have to do something to change things, learn from our mistakes," he said.
"We got off poorly and it's our own fault," he said.
Madrid will take on Villarreal away on Sunday in their next La Liga game.