Three days after winning the UEFA Super Cup on penalties against Villarreal, adding to May's UEFA Champions League triumph, the Blues dominated against Palace from start to finish.
Christian Pulisic was brought into the side as one of five changes from that midweek cup win and scored before half-time to add to Marcos Alonso's 27th-minute opener.
Palace's first game under Patrick Vieira went from bad to worse as Trevoh Chalobah marked his league debut for Chelsea with a superb goal, giving the returning home fans plenty of reason to celebrate.
Goalscorers Alonso and Pulisic combined early on as the latter glanced a header on target for Vicente Guaita to keep out.
Mason Mount tested Guaita from a free-kick, but the Palace shot-stopper could not get anywhere near Alonso's attempt, the wing-back curling the ball over the wall and into the net from 25 yards.
That was Chelsea's 50th direct free-kick goal in the Premier League – only Manchester United (64) has more – and it deservedly doubled its lead in the 40th minute.
Guaita spilled Mount's low cross from the right and Pulisic took full advantage by firing home the loose ball from close range.
Chelsea did not take its foot off the gas and had a third goal before the hour mark thanks to academy graduate Chalobah's long-ranger that went in off the left-hand post.
The hosts continued to threaten without finding a way through, but Tuchel would have been equally pleased with a first clean sheet in five league games stretching back into last season.
Chelsea faces rival Arsenal in eight days' time, while Palace hosts newly promoted Brentford, which beat the Gunners in its Premier League opener, next Sunday (AEST).