Cristiano Ronaldo set up the Brazilian playmaker in the 82nd minute for a first-time strike high into the net, his first goal this season in only his third appearance after coming back from a knee operation.
"This is what I needed, to return to play here at the Bernabeu, to score a goal and for the team to win the game. It's a happy night for me," Kaka told reporters.
"It was a difficult game and they played very well, but we managed to equalise before the break after a first half in which we struggled. In the second half we got the goals we needed."
Kaka, who had played the last 15 minutes away to Getafe in the league and Levante in the King's Cup, was thrown on in the 70th minute and wrapped up the match to a huge roar from a packed Bernabeu.
Sunday's win left them two points short of the champions, with one match to play before the mid-point of the season.
