Anthony Pilkington gave the visitors a 13th-minute lead with a clinical close-range finish, but Jermain Defoe levelled 12 minutes before half-time, chipping his shot over Norwich goalkeeper John Ruddy.
But Paul Lambert’s side sealed a memorable victory when Elliott Bennett rifled a low shot past Brad Friedel from outside the area in the 66th minute.
“Credit to them as I think they deserved it,” said Tottenham manager Redknapp.
“We were disappointing. I changed the system to 4-4-2 and we were too open. I thought they bullied us a little bit.
“It was a difficult day for the boys at the back. It was a bad day but we have to pick ourselves up.”
Spurs’ defeat leaves the north London outfit ahead of fifth-placed Newcastle United on goal difference as Redknapp’s side look to secure Champions League football for next season.
Meanwhile, Norwich moved into ninth place courtesy of their victory and Lambert heaped praise on his side after their first win at White Hart Lane since 1993.
“That was phenomenal,” said Lambert. “From start to finish we were brilliant. I told the players I have seen some big games in my time and that was colossal.
“We’ll try and finish as high up as we can. We’ve beaten a top four side, which is incredible for us away from home. I have targets in my heads.
“The obstacles I’ve put in front of my lads they’ve always jumped them. Top 10? I don’t worry about. I just want to be safe.
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