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.