Everton dominated proceedings in the opening 45 minutes and would have been disappointed to go in at the break with nothing to show for their efforts.
Ancelotti’s men controlled possession from the outset but lacked a final ball and had to settle for chances from set pieces.
Their first opportunity came from a Gylfi Sigurdsson delivery, but a combination of Yerry Mina and Mason Holgate were unable to force the ball home.
As the half progressed, Everton started to enjoy more of a presence from open play and Dijbril Sidibe was unlucky not to open the scoring when Nick Pope’s leg denied him.
Burnley were unable to find a foothold in the clash and went in at the break without a single effort on target.
Everton’s intensity dropped slightly in the second half and they possibly need to build up their fitness levels to meet Ancelotti’s demands over 90 minutes.
They continued to ask questions, however, with Bernard going close and Calvert-Lewin forcing Pope into a save.
The match looked destined to finish goalless but Sidibe, who arguably had his best game in an Everton shirt, set Calvert-Lewin up for what proved to be the winner.
Calvert-Lewin got ahead of his marker at the near post and his diving header crossed the line with some help from the far post.
Burnley were unable to force their way back into the match with just 10 minutes left to play as Everton saw things through in a professional style.
Everton are now unbeaten in four and have opened up a four-point cushion from the relegation zone after climbing up to 13th.