The Spanish midfielder returned from injury in Madrid's 7-3 win over Sevilla on October 30, coming off the bench to play 28 minutes, and has started the next four matches as the capital club have gone on a five-game winning streak.
Madrid have moved to within three points of La Liga leaders Barcelona and Atletico Madrid, while they have not lost in seven matches in all competitions.
Ancelotti compared himself with Alonso, although the former Roma and Milan midfielder accepted that the 32-year-old is a better passer.
"I can say that Xabi Alonso has been the key to this (winning streak)," the Italian head coach told esRadio.
"He is a very important player for this team and his quality and experience is vital.
"He has the ability to see the bigger picture and I can see a lot of myself in him, although if I had to compare us then his quality of pass is better. He's slow like me but is technically superior and doesn't have a problem with age.
"Take (Andrea) Pirlo, who is similar. At 35 he is still doing well and in their position age doesn't matter, yet for others it could. At right-back, for example, you need to be right physically and in peak condition.
"In the middle it is more about skill, intelligence, tactical know-how and is not as physical."
Ancelotti wants Alonso to sign a new contract with Madrid as the Spain international's current deal expires at the end of the season.
"I believe everybody knows how important it is but I'm not concerned, although it would make a great Christmas present for me if Xabi renewed," Ancelotti said.
