The Portugal forward took his league tally for the season to 31 goals, netting in his eighth successive game in all competitions, and set up Gonzalo Higuain for Real's third.
Coach Jose Mourinho has said Real's title defence is effectively over but fielded a near full-strength side at San Mames as they moved on to 68 points, 13 short of leaders Barcelona with seven games left to play.
Ronaldo was at the centre of much of the attention and reacted by outjumping his marker to thump Xabi Alonso's free kick past Gorka Iraizoz in the 68th minute.
Like Real, Barca's priority is to conserve their energies for the Champions League semi-finals in two weeks' time, and they rested a host of players in Zaragoza including Lionel Messi, Andres Iniesta and Gerard Pique.
"We miss Messi, obviously, but we have some great players with a lot of football in their boots," Thiago told Spanish broadcaster Canal Plus.
"We would like to win the league as soon as possible but there are still many games left to play. The title isn't won yet."
The Colombia striker, constantly linked with a move to Europe's top clubs, took his league tally for the season to 24 as Atletico moved on to 65 points in third, three short of next month's King's Cup final opponents.
Atletico were ahead after only four minutes at the Calderon when Diego Costa headed in Koke's cross, and the Brazilian striker set up Falcao for the second after a swift counter-attack.
