The home side gave Madrid a guard of honour as they ran out but that was where the welcome ended as the 34-year-old Cazorla opened the scores on four minutes with a snap shot from 18-yards out that caught Thibaut Coutois cold.
It was the first Liga goal of 2019 and Cazorla's first ligue goal since 2012.
But the Frenchmen Karim Benzema and Raphael Varane both bagged flashing headers as Real swept back into the lead with Brazilian midfielder Casemiro and Ballon d'Or Luka Modric pulling the strings in midfield.
Benzema latched on to an inch perfect Lucas Vasquez cross to head home unmarked from the back of the six-yard box.
German midfielder Toni Kroos was at the origin of Madrid's go ahead goal as he picked out Raphael Varane at the far post and the Frenchman finished with a towering header.
Modric had the ball in the net on the half-hour but the video assistant referee proved he was off side for his shot.
Cazorla was to have the last word when he ran from deep to produce an unmarked header of his own and level the score with the clock running down in the Estadio de la Ceramica.
Sergio Ramos still had time to pick up a yellow card for elbowing a rival, sending the yellow clad home fans into howls and boos as Villarreal earned a precious point for their relegation worries.