Captain Sergio Ramos broke the deadlock in the 24th minute and the excellent James Rodriguez and Cristiano Ronaldo added goals either side of a header from visiting forward Juanmi.
Ronaldo's 50th goal of the season – the fifth consecutive campaign in which the Portuguese superstar has reached this milestone – arrived in stoppage time after he struck the post with an earlier penalty.
But a Real attack already missing Karim Benzema due to a knee problem was shorn of Gareth Bale inside the first five minutes after the Wales international went the turf clutching his left calf.
In the second half, midfielder Luka Modric suffered a painful blow to his right knee in a challenge with Recio before being substituted, leaving Ancelotti sweating on the fitness of the duo ahead of Wednesday's UEFA Champions League quarter-final second leg showdown with Atletico Madrid.
"Modric has a knee problem and Bale calf but we cannot say more for now, we have to assess them in the coming days," the Real coach explained.
"They are not completely excluded [from the Atletico game]. We must conduct examinations and assess all this."
Ancelotti did sound a note of optimism over Benzema's prospects of being involved next week, when Real will look to edge out their neighbours at the Santiago Bernabeu having shared a goalless first leg.
"He will be there, his condition is improving," the Italian said of Benzema.
"We have four days ahead and the possibility that he recovers well."
Real remain two points behind La Liga leaders Barcelona after their bitter rivals claimed a 2-0 win over Valencia earlier on Saturday and Ancelotti hopes the tussle for the title goes right down to the wire.
"I hope the title isn't decided before the last day," he added. "We're still in the title race and both teams have tough games because there's lots at stake for everyone.
"Barca have the advantage, but we'll try to do well in all our remaining matches."
