Van der Vaart, who joined Spurs on deadline day for £8million, produced another virtuoso performance to ensure the hosts avoided a European hangover.
The 27-year-old scored both his side's goals as they came from behind in the latest White Hart Lane thriller.
"He's started well; he's going well; he's going great," manager Redknapp said after watching Van der Vaart score his fourth goal in his third home appearance for his new club.
"He's always looking to get on the ball and he's always looking to score. He's got that knack of scoring goals."
Van der Vaart has instantly made himself a favourite among his new fans.
Redknapp said: "He's a good footballer and they always like a good footballer."
After coming to his side's rescue against Wolves two weeks ago and against FC Twente on Wednesday night, Van der Vaart was at it again this afternoon.
Villa capitalised on another slow post-European start from Redknapp's men when Marc Albrighton gave them the lead with his first professional goal.
But Van der Vaart headed in a crucial equaliser in the third minute of first-half stoppage-time before rifling home a 75th-minute winner.
The second goal came after Redknapp switched him the midfielder from the right wing to a more central role at half-time, sacrificing striker Roman Pavyluchenko.
Redknapp said: "I felt, first half, we were open, too open, with two up and him floating around where he wanted to play.
"Second half, we changed it and I stuck him in behind one striker."
Spurs were ripe for the counter-attack in the first half, especially with Tom Huddlestone playing as a makeshift centre-back.
Redknapp, who had only one recognised defender fit in Sebastien Bassong after Ledley King failed a late fitness test, said: "We're short of central defenders. I had to play Tom back there today and I just felt that we were open all the time.
"We went for it a little bit, really."
Villa's defeat was Gerard Houllier's first since taking charge after he claimed victories in his opening two games in the dugout.
The former Liverpool boss was unhappy with the amount of first-half stoppage-time played by referee Mark Clattenburg, who allowed more than the minimum of two minutes he had indicated, giving Van der Vaart the time to level.
"I was just not happy with the equaliser because the game had elapsed quite a long time after the two minutes which were indicated," Houllier explained.
"But that's the referee; the law says it's a minimum of two minutes. He decided it was three minutes."
The Frenchman also felt the visitors should have been awarded a penalty for a foul on Emile Heskey, who went on to set up the opener.
The former England striker injured himself laying on Albrighton's 16th-minute goal and was replaced 10 minutes before half-time by John Carew.
Revealing Heskey merely had a dead leg, Houllier said: "Don't get me wrong, I think John Carew did a good job but, probably, it's not the same player.
"I've got mixed feelings because, at the same time that I'm proud of their performance, I'm disappointed with the result. A more fair result would have been a draw."
He added: "The only thing we can blame ourselves for is probably the fact that we didn't take our chances. A couple of times, we could have sealed the game."
Admitting Spurs are "slightly superior" as a team to his side, Houllier said: "It's a good side, a good team; they finished fourth.
"On the back of their win against Twente, obviously they have a lot of confidence."
He added of Van der Vaart, whose two goals were set up by Peter Crouch: "I think he was outstanding but Crouchy was good as well."