Spurs were facing a third home defeat on the spin after Rodrigo fired home with a little over 10 minutes to play, but the Argentine’s quickfire double sent Spurs into the mid-season break looking at the table.
Leeds, who had led early on through the in-form Crysencio Summerville, ended the match with 10 men after Tyler Adams was shown a second yellow card in the closing stages.
Tottenham had twice come from behind to level, with goals by Harry Kane and Ben Davies. There was concern late on for Pierre-Emile Hojbjerg, who appeared to be hobbling in the closing stages after a heavy challenge.
Victory lifted Tottenham into third place with 29 points, before Newcastle hosted Chelsea, with Leeds on 15 points in 14th place.