Adam Webster had given the visitors a richly deserved lead, heading in from Pascal Gross’ right-wing delivery towards the end of the first half.
However, Spurs, who played at a pedestrian pace during the first period, raised their tempo after the interval to fight back.
Harry Kane levelled matters with a right-foot shot into the bottom left corner after Brighton goalkeeper Mat Ryan had brilliantly parried his first effort.
And Dele Alli’s sublime lobbed finish then found the top left corner to complete the turnaround.
It ensured Brighton’s miserable record on 26 December continued – with the Seagulls now winless in their last 11 games on this date.
