Red cards for Cristian Romero and Destiny Udogie left Tottenham with nine men for much of the game and Chelsea took full advantage.
The Senegalese striker put Chelsea ahead in the 75th minute when he finished off a counter-attack, before adding two similar goals in injury-time to seal the win.
After his third strike, Jackson performed Cristiano Ronaldo's iconic celebration in front of the travelling Chelsea fans.
Tottenham put in a heroic shift to keep Chelsea at bay for much of the second half, but their lack of discipline and extremely high defensive line cost them.
Defeat saw Spurs surrender top spot in the table to Manchester City, while Chelsea rose to 10th.
On Saturday Tottenham will travel to Wolves, while Chelsea will host Man City at Stamford Bridge.
