Ancelotti endured a miserable return to Stamford Bridge last season with his current employer, Everton going down 4-0 in the capital on that occasion.
But he came out on top in a second meeting with Frank Lampard, who was part of the Chelsea squad that secured a domestic double under the Italian coach in the 2009-2010 season.
The only goal of the game arrived in the 22nd minute thanks to an early Christmas gift from Edouard Mendy, the goalkeeper needlessly charging into Dominic Calvert-Lewin as the striker attempted to get on the end of his own flick-on from Jordan Pickford's long punt.
Sigurdsson calmly rolled in his attempt from the spot for his first league goal in 17 games, much to the delight of the 2000-strong crowd allowed inside Goodison Park.
Chelsea responded brightly to the setback of falling behind, Reece James striking a post with a low drive that Pickford appeared to get a slight touch to, while Kurt Zouma – who spent a season on loan at Everton earlier in his career – planted a close-range attempt straight at the England goalkeeper.
Richarlison failed to capitalise on a clear shooting opportunity before the break for the hosts, slipping as he struck the ball with his left foot to make Mendy's life easier.
Sigurdsson went close with a free-kick early in the second half and was then denied the chance to take another penalty when a VAR (video assistant referee) check found Calvert-Lewin offside prior to being bundled over by Ben Chilwell.
Still, one goal proved enough as Chelsea failed to find an equaliser, despite Lampard sending on Tammy Abraham in place of the ineffective Kai Havertz to partner Olivier Giroud up top.
Mason Mount saw a free-kick kept out by a post as Everton held firm, in the process securing a third successive home win over its opponent as it moved into the top half.
