Spurs trailed 2-1 going into second-half stoppage time before bettering the previous mark set by Manchester City with their dramatic 2010-11 title triumph when they were trailing at 91:12 before scoring two late goals to win 3-2 at QPR.
Tottenham were down 2-1 at 94:52, before Bergwijn bundled home an equaliser, with Kane’s throughball then setting up the Dutchman’s remarkable winner.
“We showed we don’t want to give up, never. The players know what our philosophy must be - we must fight to the end and try to get a result,” Conte told BBC after the game.
The result lifts Spurs up to fifth on 36 points, with numerous games in hand on their rivals. Tottenham have three games in hand on fourth-placed West Ham who are one point ahead while Chelsea, who they play on Sunday, are eight points ahead but have played four more games.
Spurs are now unbeaten across their past nine league games but, despite their run and situation, Conte refused to set any targets.
“We know we have a long path in front of us but for me it’s important to know they want to improve,” the Italian said. “Step by step we need to raise out level and improve quality. If I see one situation we need to improve, there are key moments that you need to control the game. A great team does this.
“For me it’s difficult to tell you something about our target. We have a long path and now we have to work. We know very well we have to fight to try to reach our best result. It will be very difficult because of the level of this tournament.”