Dominic Calvert-Lewin struck twice to end Newcastle’s nine-match unbeaten run at St James’ Park.
The 22-year-old striker, who headed the winner in Ancelotti’s opening game against Burnley on Boxing Day, shone once again as the Toffees secured a 2-1 success.
Having fired his side in front after just 13 minutes, Calvert-Lewin fumbled what turned out to be winner over the line midway through the second half shortly after Newcastle had levelled through Fabian Schar.
Everton manager Ancelotti said: “I am happy. The team is improving and that is important.
“The players are trying to adapt, they want to change a lot. The job Duncan Ferguson did was fantastic. The spirit was strong when we arrived.”
It proved a painful defeat for Steve Bruce, who restored the likes of Andy Carroll and Jonjo Shelvey having rested them for the Boxing Day thumping at Manchester United.
“I don’t think we deserved to lose,” Bruce said. “We were caught by a sucker-punch when we were going for the game.
“It is the first time since August we suffered back-to-back defeats. We have given ourselves a good platform for the second half of the season.”
Miguel Almiron, fresh from scoring his overdue first goal for the club last week, almost repeated the feat with under a minute on the clock but was let down by his final touch after being teed up by Joelinton.
After affording another chance to Joelinton, which was saved by Jordan Pickford, Everton belatedly stirred and Mason Holgate forced a fine save out of Martin Dubravka.
Four minutes later, Everton were in front. Gylfi Sigurdsson delivered a free-kick into the box at the second attempt, where it took a series of minor deflections before landing fortuitously at the feet of Calvert-Lewin to sweep home.
Schar blocked a goal-bound Theo Walcott effort to prevent Everton extending their lead as the visitors began to take control.
A change in formation around the half-hour mark lifted Newcastle, with Almiron looking much more effective in a wider role. The Paraguayan struck the post during a goalmouth scramble in the 29th minute, the ball rebounding for Carroll to prod home from close range only to be ruled offside.
Almiron then hit a rising effort of his own which was acrobatically saved by Pickford.
Moise Kean came close to extending Everton’s lead when he drilled a shot straight at Dubravka at the start of the second half, before Newcastle seized a chance to equalise.
Jetro Willems whipped in a free-kick from the left which Carroll nodded down for Schar to hook home.
Everton responded within eight minutes with a counter-attack after Carroll lost the ball on the halfway line.
Linking well with Walcott on the right, Richarlison burst clear and crossed low for the unmarked Calvert-Lewin, who scrambled the ball home from point-blank range.
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