His shot was turned in for an own goal by Ben Godfrey for the opener before the Germany international won a penalty, which Jorginho converted, to maintain Tuchel’s unbeaten record as Chelsea boss.
Havertz, 21, moved to London in a £71m transfer from Bayer Leverkusen in September but has only scored one Premier League goal and was making his first start since 27 January.
I am very pleased with Kai. It was the trust we gave him and he used that trust, who has not lost in 11 games in charge since replacing the sacked Frank Lampard in January.
He has all the ability to be a dominant figure in [attack] and he stepped up.
He showed up between the lines to accelerate our game, increase the touches in the box, be responsible for assists and through-balls, and take responsibility to finish himself.
There is no doubt about his quality, his talent and his character, said Tuchel.
Havertz also had a goal disallowed for a handball and Everton goalkeeper Jordan Pickford, who had conceded the penalty, made a number of saves to deny Chelsea a bigger winning margin.
Tuchel’s side remain fourth and in the last Champions League qualifying spot. With 10 league games of the season left, they are now only three points behind third-placed Leicester and four adrift of Manchester United in second.
Chelsea are two points ahead of West Ham, although the Hammers, up to fifth and above Everton following a 2-0 win over Leeds, have a game in hand.