In a chaotic encounter, there were five goals disallowed, three for Chelsea and two for Spurs - four for tight offsides and one because Raheem Sterling handled the ball before scoring.
Dejan Kulusevski's deflected strike gave Spurs an early lead but Cole Palmer equalised from the penalty spot after Romero's lunge on Enzo Fernandez, before Jackson punished Tottenham three times as the offside trap was broken.
Here's how we rated the Spurs players.
Unreal. Denied Jackson with outstanding saves in either half but could little about his late show.
Also made a brave block to keep out Marc Cucurella's effort, and was perfect at charging off his line to clear when Spurs were a man, and then two men, down but could do nothing about the later goals.
Pedro Porro 8
Bailed out by Vicario after his error led to Jackson's early chance. Fought doggedly and looked to lift the crowd whenever possible.
Cristian Romero 2
Lost his head. Lucky to avoid a sanction for kicking out at Levi Colwill before following through on Fernandez with his studs showing, conceding the penalty.
Micky van de Ven 7
Forced off with what looked like a serious hamstring injury. Will be an enormous miss if he is sidelined for any significant length of time.
Destiny Udogie 4
Lucky to avoid a straight red card for a lunge on Sterling before being sent off for a second late challenge on the winger with 35 minutes to play. Did not look fit.
Yves Bissouma 8
Never stopped running as Spurs tried to keep the blue tide at bay in the second half and relished the battle.
Pape Sarr 8
Made Kulusevski's goal in another encouraging, feisty display. Getting better with every game, particularly the crispness of his passing.
James Maddison 7
Made the opening goal with a pitch-splitting pass but forced off before the interval after rolling his ankle. He wanted to carry on, encouragingly.
Dejan Kulusevski 8
His work rate when Spurs had 10 (and then nine) men was phenomenal. Opened the scoring with a deflected effort.
Brennan Johnson 7
Had the run of the left flank before the game descended into chaos. Unlucky not to have an assist when Son finished his cross but was ruled fractionally offside. The fall guy after Romero's sending off.
Heung-min Son 7
Worked tirelessly but it was a thankless task at times, particularly after Udogie's dismissal. So unlucky his cool finish to make it 2-0 was ruled out for a fractional offside and nearly scored at 2-1 but Robert Sanchez made a great save.
Eric Dier (Johnson 34') 7
Excellent in his first minutes of the season and unlucky his fine strike was ruled out for offside. Struggled with the high line, as expected, but gave everything and made some important interventions
Emerson Royal (Maddison 45') 6
Put in a shift out of position at centre-half and then left-back.
Pierre-Emile Hojbjerg (Van de Ven 45') 8
Lived up to his Viking reputation with a battling display. His best moment of several defensive interventions was clearing Jackson's header off the line.
Oliver Skipp (Kulusevski 61') 6
Gave his all in an energetic performance in the middle.
Rodrigo Bentancur (Sarr 61') 6
Nearly had an assist on his home return for Dier's disallowed goal. More minutes will do him good but should have equalised from close-range late on.
Not used: Forster, Lo Celso, Richarlison, Gil.