Everton's Ross Barkley in action with N'Golo Kante
Spurs, who were still in the title race at the time, were 2-0 up in the Premier League game after 44 minutes.
Chelsea launched a comeback in the second half, with Gary Cahill pulling one back for the home team just before the hour mark.
With just seven minutes of normal time remaining, Belgium international attacking midfielder Hazard scored the equaliser for the Blues.
The 2-2 draw at Stamford Bridge saw Leicester win the Premier League title.
Kante, who left Leicester for Chelsea in the summer transfer window, has revealed his conversation with Hazard about that goal.
“I was with the team at Jamie Vardy’s house and when we saw Chelsea losing 2-0 at half-time against Tottenham, we said now we have to be ready for the Everton game, but at the end this was a very good night,” Kante told Chelsea’s official website.
“When I saw Eden Hazard here at Chelsea I said to him you maybe do not know but everyone thanks you.”
Kante was one of the best players for Leicester last season and was a key figure in the Foxes’ Premier League title triumph.
The 25-year-old France international midfielder cost Chelsea a transfer fee of £30 million, according to BBC Sport.
Danny Simpson and N'Golo Kante in action with Wayne Routledge