Crouch, with England manager Fabio Capello watching on, nodded in a rebound after 82 minutes to spark wild celebrations among fans who had travelled up from North London to see their team book a place in the Champions League qualifiers.
City would have leapfrogged Tottenham with a victory but could have no complaints as the visitors carved out the better chances in a match of gut-wrenching tension at Eastlands.
The North London club, who like City have lived in the shadow of their neighbours for so long, have not appeared in Europe's top club competition since 1962, a year after they last won the English title.
"We came here to a hot atmosphere and got at them and we deserved the win," Redknapp told Sky Sports before his ecstatic players drenched him with a bucket of water.
"It's been a terrific season for us, we've played some great football and we deserve it. I thought the goal wasn't going to come and we'd go to Burnley with the extra point in the bag, which would have been a good situation, but this is perfect."
While Redknapp celebrated after a ninth win in 11 league matches, City boss Roberto Mancini trudged away with the consolation of a place in the Europa League, not what the club's Abu Dhabi owners who watched stony-faced had hoped for when they hired the Italian in place of Mark Hughes in December.
"I think you could see what it means," King told Sky Sports. "The fans have waited a long time for this."
City striker Carlos Tevez set about the game with gusto, running at the heart of Tottenham's defence and forcing Benoit Assou-Ekotto into a desperate block.
The visitors responded with King having a headed goal disallowed shortly after Crouch struck the post with a header from Gareth Bale's cross.
Tottenham's Brazilian keeper Heurelho Gomes, a doubt before the game with a groin injury, reacted well at the other end to beat out a fierce shot by Ad
