Iker Casillas comes off bench, helps Real
Casillas, however, was thrown into the action after just seven minutes when Adan was shown a straight red card for bringing down Sociedad forward Carlos Vela inside the area to concede a penalty.
Real Madrid eventually stormed back to sink Sociedad 4-3 at the Bernabeu thanks to Cristiano Ronaldo's two second-half goals.
Mourinho caused a major stir in Madrid's final match of 2012 against Malaga when he dropped long-serving number one and captain Casillas in favor of Adan.
Mourinho said after the 3-2 loss to Malaga that his decision to select the 25-year-old Adan in place of the Spain skipper was "purely technical'' and insisted he did not regret dropping Casillas, despite defeat leaving them 16 points behind Barcelona in La Liga.
Adan was overwhelmed in that game when he conceded all three goals in the one-goal loss, and he was shown to be out of his depths at home on Sunday as well.
The regular backup made a poor pass that Vela intercepted, and he then charged out and tackled the Mexico forward in his box.
The referee didn't hesitate to show him a direct red card, creating the dramatic situation of Casillas being called off the bench to defend the penalty try.
The crowd chanted "Iker! Iker!" as the Spanish international jogged on, but there were no heroics as Prieto coolly stroked in the spot kick to equalize in the ninth.
Mourinho had kept his cards close to his chest when asked Saturday whether he would recall Casillas for Madrid's opening match of 2013 against Sociedad, but it was confirmed Sunday afternoon he had decided to stick with Adan.
Information from Press Association and The Associated Press was used in this report.