Real broke the transfer record when they paid Tottenham Hotspur 100 million euros (£86m) to sign the Wales winger earlier this month and he struck in the 38th minute at the Madrigal to make it 1-1.
The 24-year-old, included in the starting line-up after training with his team mates for the first time on Wednesday, made no mistake from close range, holding off his marker and clipping a Dani Carvajal cross into the net.
It was a dream start, particularly as he is short on fitness after his preparations for the season were disrupted by the protracted negotiations over his move, and he was replaced by Angel Di Maria on the hour.
"I think he is happy because scoring the first goal for Real Madrid is very good for him," Ancelotti said at a post-match news conference.
"It was a difficult game for him, as for all the players, but he showed a good attitude on the pitch," the Italian added.
Clad in Real's all-white kit and wearing the number 11 shirt, he overhit a cross that sailed harmlessly out of play in the 18th minute before switching with Ronaldo and moving over to the left wing.
Before Bale's move, Ronaldo was the most valuable player in soccer after he joined Real from Manchester United for £80m in 2009.
Comparisons between the two have inevitably been made and Ronaldo matched Bale by scoring Real's second in the 64th minute before Giovani Dos Santos, another former Tottenham player, made it 2-2 in the 70th minute.
Ronaldo needed 35 minutes to open his account for Real on his La Liga debut in August 2009, scoring a penalty in a 3-2 win at home to Deportivo Coruna.
Real return to training on Sunday to prepare for Tuesday's opening Champions League game at Turkish rivals Galatasaray in Group B. ($1 = 0.7542 euros)