It also kept Spurs on course for their first FA Cup final since 1991.
Defoe gave Tottenham a 37th-minute lead with a mis-hit shot that looped over Leeds goalkeeper Casper Ankergren and, although Luciano Becchio hauled the home side level in first-half stoppage time, Defoe struck twice more in the second period.
His decisive second, when he swept home David Bentley's cross, came in the 73rd minute and he coolly slotted home a third - his 23rd of the campaign - after rounding Ankergren in time added on.
Redknapp, who tasted FA Cup glory with Portsmouth in 2008, said: "It was nice to see him get his hat-trick. He could have scored six tonight in fairness. He had some great opportunities.
"He took three great finishes and missed three that were maybe easier, but he was always in the right place, he was always a threat. He's a goalscorer."
Redknapp, told earlier in the day his own horse, Arry's Orse, had won at Lingfield Park, had tipped Defoe to become a top-class goalscorer when he first saw him play.
The former West Ham and Pompey manager added: "He's always scored goals. I signed him as a 15-year-old and every Saturday I used to watch him in the youth team and he used to get hat-tricks, or score every week anyway. He's done it since he was a little boy."
Redknapp felt Leeds' equaliser was clearly offside and dealt a big blow to his players, coming just before the interval.
He said: "We had to pick ourselves up again for the second half, but when we kept the ball and passed the ball I thought we played well.
"Now we have another tough game at Bolton. It's not an easy place to go, but we're playing very well. We've had one defeat in 13 games."
Redknapp, who had joked after the 2-2 draw at White Hart Lane that a trip north to face Leeds was just what he had wanted, was full of praise for the Yorkshiremen, who had pushed his side all the way after their famous third-round upset at Manchester United.
"These are difficult games," Redknapp added. "I've won and lost these games when you're fancied to win.
"We came to Elland Road - probably the first time for some of my players. The atmosphere the fans created was just incredible.
"This is a massive football club. It's really a Premier League club and it needs to get back where it belongs.
"Leeds are a good side and they'll certainly go up this year and I can see them being back in the Premier League in the next few years."
Leeds boss Simon Grayson did not carry the look of a crestfallen manager and was clearly proud of his players' performance.
He said: "We were very good again. We passed the ball around well and competed ever so well against a top team in the Premier League.
"That's all we said to the players - give a good account of yourself and do yourselves justice.
"Nobody expected us to win apart from maybe 33,000 inside the ground and the players, but we like to think we've come out of it with a lot of credit."
FA Cup 09/10 Win Outright: Tottenham 11/2