Kane scored an 89th-minute winner after also levelling the tie at Wembley to maintain Tottenham's hopes of qualifying for the knockout stages.
Had Tottenham lost to PSV, which looked likely when Luuk de Jong scored after two minutes, their Champions League campaign would have been hanging by a thread.
Redknapp, who managed Kane for three years, said Mauricio Pochettino has come to rely on the striker at key moments.
"Time and time again he pulls them out of trouble. He's an incredible finisher. What a player. What a captain. What a leader," Redknapp said on 'BT Sport'.
Redknapp also revealed that he had been aware of Kane as a young player.
"He played in Europe for me when I was there. We always felt he was going to be - we couldn't say he was going to reach the heights he's reached, you couldn't guarantee that," he added.
"But certainly the people at the club who were working with him on a daily basis - Tim Sherwood, Les Ferdinand... he was in their group and they were so confident he was going to be a top class player and that's what he's turned out to be. (He's) a special player."