Antonio Conte's side appeared to be signing off before the World Cup with a third successive home league defeat as Leeds led 3-2 with less than 10 minutes left thanks to Rodrigo's brace.
But Bentancur's deflected shot made it 3-3 in the 81st minute and two minutes later he was set up by Dejan Kulusevski for a simple finish to leave the visitors empty-handed.
Victory lifted Tottenham into third place with 29 points from 15 games with Leeds on 15 points in 14th place.
Tottenham's habit of starting slowly returned to haunt them as Summerville's fourth goal in as many top-flight games put Leeds ahead in the 10th minute.
Leeds regained the lead on the stroke of halftime when Rodrigo fired past Lloris following a corner.
Davies made it 2-2 early in the second half, reacting well after Kane's goalbound effort was blocked by Rasmus Kristensen.
Leeds continued to threaten though and took the lead for the third time when Rodrigo's shot crept in at the far post with Tottenham appealing for a foul in the build-up.
Tottenham dredged up one final effort, though, and Bentancur proved the hero to secure a victory that consolidates their place in the top four.