Chelsea took the lead when Moises Caicedo stole the ball from Micky van de Ven on the edge of the Spurs penalty box and the combative Ecuadorian squared for Joao Pedro, who made no mistake from eight metres in the 34th minute.
The 24-year-old Brazilian had chances to add to his goal tally but was thwarted three times by Spurs goalkeeper Guglielmo Vicario, who also denied Pedro Neto and Alejandro Garnacho.
"I needed this goal because it had been a long time I didn't score, and the team expect that from me," Joao Pedro said.
"I always want to help the team with goals and assists, but first I need to play well. If I play well, the goals are going to come. The important thing is just to win games, and I am very chill about the goals."
Joao Pedro, who last scored in August, said he was focused on contributing to Chelsea's collective play rather than chasing personal milestones.
"In my position, if you don't shoot, you get frustrated, but you need to not look just at yourself. You need to see if the others can get a chance," he said.
"If I don't shoot, I am going to create space for the others... I play for the team. If we just win, I am happy. Of course I want to score, but sometimes it's not going to happen."
Chelsea visit Azerbaijan next to face Qarabag in the Champions League on Wednesday before hosting Wolverhampton Wanderers in the Premier League on Saturday.