Enzo Maresca's men, stung by last weekend's home defeat by Sunderland, stifled Spurs and created a string of chances which should have allowed them to win by a bigger margin.
The Blues took the lead when Moises Caicedo stole the ball from Micky van de Ven on the edge of the Spurs penalty box and the impressive Ecuadorian squared for Joao Pedro who made no mistake from eight metres in the 34th minute.
The 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 while his opposite number Robert Sanchez had only one save to make.
The home fans vented their frustration at Thomas Frank's side as they failed to mount any real threat and loud boos rang out around the Tottenham Hotspur Stadium on the final whistle.
Chelsea climbed to fourth place in the table on 17 points after 10 games, one rung below Spurs on goal difference.
Spurs have now registered just one win against Chelsea in their last 14 Premier League meetings and the visiting supporters treated their hosts to a chant of "Tottenham Hotspur, it’s happened again" in the dying moments of the game.