Chelsea, who won three league titles under Mourinho, spent long periods camped in the Spurs half but struggled to break through the disciplined defending — a trademark of Mourinho’s coaching prowess.
The visitors threatened in the first half on the break, pouncing on any error to flood forward at speed.
Tottenham right-back Serge Aurier forced Chelsea goalkeeper Edouard Mendy into a save with a fierce shot in the 15th minute, and left-back Sergio Reguilon also stretched the hosts.
Chelsea sought to start the second half on the front foot and right-back Reece James swung in two crosses but Tammy Abraham failed to connect with either.
A shot by Mason Mount was heading for the bottom corner in the 81st minute but was tipped wide by Spurs keeper Hugo Lloris.
In added time, Chelsea substitute Olivier Giroud was unable to capitalise on an error by Welshman Joe Rodon on his Spurs debut as the French striker hit a tame shot straight at Lloris.
The result took Spurs back above Liverpool on goal difference at the top of the table with both sides on 21 points, two ahead of third-placed Chelsea after 10 games.
Premier League (EPL) Points Table: