Richarlison headed home fellow substitute Ivan Perisic’s corner and Kulusevski fired the winner to spark wild celebrations from the home crowd.
Spurs had looked set for its first league defeat of the season when trailing to Gustavo Hamer's 73rd-minute goal.
But the London club secured its fourth win of the season to stay second, behind leader Manchester City.
Richarlison struck in the eighth minute of stoppage time and Kulusevski hit the winner two minutes later to maintain coach Ange Postecoglou's impressive start at the club, which saw him win manager of the month for August.
Sheffield's Oli McBurnie was sent off for a second yellow card in the 14th minute of stoppages.
The Blades remain winless after five matches.
The visitors were in front when Spurs failed to deal with Jack Robinson’s long throw that dropped for Hamer, who drilled in at the back post via the woodwork.
Postecoglou reacted with a triple substitution in the 80th as deadline day signing Brennan Johnson, Richarlison and Perisic were brought on.