Record signing Lukaku was dropped for last Sunday's Premier League draw with Liverpool after comments he made in an interview recorded three weeks ago, saying he was not happy with his role at the club and would like to return to Inter Milan.
After holding clear-the-air talks with Tuchel he returned for the League Cup semi-final against Tottenham Hotspur on Wednesday.
Tuchel made several changes to his Chelsea side as he juggled a hectic schedule and COVID-19 infections, giving debuts to keeper Marcus Bettinelli and youngster Lewis Hall.
But his side were still too strong for Chesterfield as Chelsea made it 24 wins in a row in the FA Cup third round.
"I'm happy with the attitude and how we started," said Tuchel. "We started strong and decided the match very early. This is what we wanted."
Chesterfield manager James Rowe said Asante's goal gave the club something special to remember.
"Great to get the goal at the end for us and the supporters and what a proud day to be a Spireite," he said.
"Halftime was about recollecting our thoughts. We focused at halftime and drew the second half 1-1."