The 18-year-old, who made his first appearance for the first team at Wolves earlier in the month, was brought into the starting line-up for a tough game against a team that were chasing European football.
Branthwaite played alongside Michael Keane at the heart of the Everton defence and was influential in the Blues keeping a clean-sheet and picking up three points on the road.
Everton have to be patient with Branthwaite
After a first-half of very few chances between the two sides, Everton took the lead just 56 seconds after half-time when Richarlison found the far corner of the net when he glanced Gylfi Sigurdsson’s free-kick home.
At the other end of the pitch, the Blues dealt with everything that was thrown at them and ensured the Blades didn’t have a shot on target during the 90 minutes.
Ancelotti believes this is “just the start” for Branthwaite and spoke about his scouting department, who recruited the youngster from Carlisle United earlier this year.
"It was a good performance, focused,” Ancelotti told reporters in his press conference. “What surprised me is the fact that, when he makes a mistake, he never loses confidence. He's always there focused, concentrating, calm.
"He has a really good character apart from the quality he is able to show. It's just the start. As I've said before we have to be patient with him, but he's a really good defender. Good with the ball, always focused.
"I know his character. He's really focused and humble. It's a pleasure for us to have this young player.
"I have to say that our scouting department did a fantastic job finding him in a lower division."
The fantastic spirit can be a good sign for the future
There have been questions asked about this Everton side, who went four games without a win in the league, which brought an end to any hopes of European football next season.
Ancelotti opted for a midfield three of Sigurdsson, Andre Gomes and Tom Davies and the trio looked compact throughout. The Everton boss said the team looked dangerous on the break and praised the “fantastic spirit” of his players.
Ancelotti said: "The spirit was really good. It is not a surprise. The players know really well what our supporters ask for on the pitch - to have a good spirit and fight and we showed that today.
"We had opportunities on the counter attack, I am really pleased with the performance. We are at the end of the season, but this fantastic spirit can be a good sign for the future.
"Since December we did quite well. We lost a bit of motivation for the last few games, but it is important to finish well. A win here is important."
The Blues will round off their Premier League campaign by welcoming relegation-threatened Bournemouth to Goodison Park on Sunday afternoon.