Ancelloti, managing the Spanish giants for the first time after replacing Jose Mourinho this summer, introduced the forward at the break and he took just two minutes to score Madrid's fourth in an emphatic victory at Dean Court.
And the Italian confirmed he wants the forward - who has been closely linked with both Arsenal and Chelsea as well as Napoli - to stay and that until he hears otherwise he will be treating Higuain as one of his first-team squad.
"Not true, I don't have any news about this," he said at the press conference when asked to confirm whether a deal had been agreed with the Italian club. "I think that now we have to speak about Higuain as a Real Madrid player. He is a fantastic player and a fantastic striker who took one minute to score tonight. I spoke to him this week. He is a Real Madrid player and until we have news we have to consider him as a Real Madrid player and I would like him to stay with us. He is very important to us and nothing else - it is not my business to judge the price of a player."
Cristiano Ronaldo netted the first two goals of his new manager's reign and predictably talk soon turned to the importance of a player so revered on these shores from his time at Manchester United.
Ancelotti explained how he sees his number seven as the most important player at the club amid rumors this week that a new deal is on the way for the Portugal international.
"I think Ronaldo is the most important player in this team because he is the player with the best quality," he said. "I think we will help him every time to do his best because if he does that every time we have a great opportunity for this season. His future is at Real Madrid, there is no question about this."
The Cherries started strongly and more than held their own for the first 20 minutes but after Ronaldo's double Sami Khedira scored on the stroke of half-time.
Higuain's early second-half strike was added to by Angel Di Maria and then Casemiro as a capacity crowd enjoyed a rare chance to see some of the world's best players at Dean Court.
But despite the quality of the opponents Bournemouth boss Eddie Howe revealed his dressing room was still an unhappy one at the final whistle.
"The feeling after was disappointment," he said. "No one wants to get beaten and no one wants to lose. It is a horrible feeling no matter who you lose to. We are not downhearted but we are disappointed. From our perspective we knew it was going to very difficult and we didn't want to change anything too much so we could test our players with our style of football.
"For the first 20/25 minutes we took the game to them until the first goal, it was a great experience for our lads. The club has been through so much in recent years - these are good days for the club. Hopefully everyone enjoyed today and enjoys this year as it is not often the club has played at this level. It is not every day you get to see Ronaldo at Dean Court."