It was a slow start from both sides with half-chances from Danny Rose, Cesc Fabregas and Diego Costa before Kane and Son fired them into a significant lead going into the break.
Guus Hiddink's side were back in it at the beginning of the second period with Gary Cahill pulling one back just before the hour mark. Willian and Ryan Mason had further opportunities but Hazard's effort ended Spurs' minimal title hopes.
Slow and steady
Spurs stepped onto the Stamford Bridge pitch knowing that anything less than a win would hand the title to Claudio Ranieri's side but despite the significance of the match, both sides were slow to get going.
Rose had the first real chance of the evening as he tried from distance and the full-back is known for scoring some screamers but this one just sailed over the crossbar.
Chelsea made good of their play on advantage in the 26th minute when the ball came to Costa who played it across to Fabregas and the Spaniard midfielder looked to place it in the bottom corner but it was just wide.
It was then the turn of Costa to have a shot on goal as he made use of Rose's mistake but his shot from distance had to be tipped over by Hugo Lloris.
Still in the race
As the minutes continued to tick by Leicester's grip on the title grew firmer but Spurs kept their ambitions alive with two goals before half-time.
Kane had been excellent throughout the campaign and he was at it again as a brilliant through ball from Christian Eriksen spilt open the Chelsea defence and Kane's run was perfect to take it beyond Asmir Begovic and tap into an empty net.
It could have been two in the 38th minute when a good ball across the area met Erik Lamela but his effort was blocked brilliantly by Cahill and Son missed the follow up.
Mauricio Pochettino's side scored the crucial second goal two minutes from the end as Eriksen once again produced a great ball after Branislav Ivanovic's initial error and the through ball this time found Son who slotted beyond Begovic.
The importance of the occasion was clear to see as a confrontation towards the end of the half broke into a mass brawl involving Pochettino himself but referee Mark Clattenburg managed to keep a lid on proceedings.
On the edge
Two goals to the good is never a score line that is set in stone and the home side jangled Tottenham nerves as they got a goal back just before the hour mark.
It was poor defending from the best defence in the league as Cahill was allowed to break free at the corner and defender's first touch was brilliant to take the pace off the ball and his second struck the volley beyond Lloris.
The current champions had the bit between their teeth as they looked to grab the equaliser as they broke down the field through Eden Hazard and Costa with the Spaniard playing it Willian but the lack of pace on the curling effort made it easy fro Begovic.
Dream is over
As the game began to come to a close Spurs did everything in their power to keep their narrow lead and had the perfect chance to put the game to bed 15 minutes from time.
Kyle Walker produced a brilliant ball into Mason who was just the outside the area and had the time to set up the effort but it was well saved in the end from Begovic.
Chelsea managed to seal Tottenham's worst nightmare as they managed to equalise eight minutes from time.
It had almost been a year to the day since Hazard's last goal at Stamford Bridge and he returned to goal scoring ways in style as he somehow picked out by Costa and made no mistake as the Belgian curled it first time into the Lloris top corner to seal Spurs' fate.