Despite his costly dismissal against Real Madrid, the England striker started the game and took only 10 minutes to open the scoring with a well-taken header before Luka Modric made it 2-0.
Crouch added his second after Matthew Etherington had pulled one back for Stoke but Kenwyne Jones smashed one in off the bar to make it 3-2 just before the break.
Despite an impressive second-half performance, the Potters could not find an equaliser and Spurs were made to hold on for the narrow win.
Redemption: Peter Crouch's relief is plain to see as he celebrates scoring the opener
The Londoners will have to put in a much more disciplined performance if they are to overhaul Jose Mourinho's men with five goals on Wednesday, but the win is an important one given that they had failed to win any of their previous four league games in their pursuit of a top-four place.
Just four days after his controversial dismissal in the Bernabeu, Redknapp chose to stick with Crouch up front alongside Roman Pavlyuchenko.
Aaron Lennon failed to overcome the illness that prompted his late withdrawal in Madrid, but Tom Huddlestone and Younes Kaboul made their first appearances in five and four months respectively.
Brace: Crouch beats Ryan Shawcross to score Tottenham's third
It was a big show of faith from Redknapp to keep Crouch in the starting line-up and the reading of the striker's name over the public address system before the match was greeted with a mixture of cheers and boos from the home support.
Tottenham showed little sign that the 4-0 hammering in Spain had affected them as they started confidently on a sunny afternoon at White Hart Lane.
Gareth Bale looked lively early on and drew an impressive diving save from Asmir Begovic with a 25-yard drive.
High-flyer: Luka Modric (L) celebrates his goal with Gareth Bale (R)
The Welshman then crossed for Pavlyuchenko but Robert Huth put in an important block to deny the Russian from eight yards.
Spurs opened the scoring 10 minutes in when Pavlyuchenko whipped in a cross from a short corner and Crouch powered a header past Begovic from eight yards.
The towering hitman, clearly delighted to have scored, ran over to the home fans with his arms aloft to celebrate.
Spurs pushed for a second and it came just seven minutes later. Pavlyuchenko played Modric and the little Croatian breezed past his two markers before slotting the ball between Begovic's legs from for his third of the season.
A Rory Delap long throw drew Spurs goalkeeper Heurelho Gomes into action for the first time, but Stoke were otherwise struggling to get into the game.
Happy return: Matthew Etherington scores against his former club
With 26 minutes gone, however, the Potters shocked the hosts with an amazing goal from former Spurs man Etherington. The winger picked the ball up on the halfway line, skipped past Michael Dawson and held off Huddlestone's challenge to go clean through and nutmeg Gomes from eight yards.
Crouch restored the two-goal cushion 33 minutes in when he climbed to reach Huddlestone's pin-point 35-yard cross and power home a well-taken header.
Redknapp was cursing his side's defending soon after though as Andy Wilkinson robbed Bale of the ball and played in Jones, who smacked a 20-yard screamer in off the bar.
Pavlyuchenko then wasted two chances and Redknapp cut a disappointed figure as he headed down the tunnel for half-time despite his side being in the lead.
Disallowed: Roman Pavlyuchenko's goal was chalked off
Gomes pulled off a good diving save to deny Jermaine Pennant from a free-kick at the start of the second period as the away side looked for an equaliser.
They soon got it when Jon Walters' close-range effort struck a post after Gomes had palmed away Jones' cross.
A cynical foul on Benoit Assou-Ekotto earned Pennant a booking in the 55th minute before the former Arsenal winger supplied Jones with a beautifully chipped cross but he headed wide.
Stoke were looking dangerous and Spurs looked anxious to add a fourth.
The ball was in the Stoke net 65 minutes in but the referee rightly ruled that Kaboul had bundled Begovic over on the line before Pavlyuchenko tapped in to an empty net.
Game of two halves: Harry Redknapp will be disappointed with his side's second half performance
Begovic then palmed away a fierce drive from Pavlyuchenko before Pulis brought Salif Diao, Ricardo Fuller and Dean Whitehead into the action with 15 minutes left.
Pennant squeezed a low shot into Gomes' hands before Bale galloped up the other end but sent a weak shot into Begovic's hands.
The Tottenham fans were becoming nervous at their side's failure to find a fourth and Jones reminded them of the threat he posed when he fired a 20-yard drive that Gomes did well to tip over.
Redknapp looked to shore up his defence by replacing Assou-Ekotto with William Gallas with three minutes left.
Gomes punched away two crosses in a nervous period of injury time as Spurs held on for the vital win.
?Spurs chief Redknapp backs Bale to land PFA Player of the Year gong Redknapp: Don't point the finger at Crouch for Real Madrid thrashingFears over future of Bale and co as Spurs chief hints at squad cutbacksAll the latest Tottenham news, features and opinion
?Explore more:People: Matthew Etherington, William Gallas, Harry Redknapp, Robert Huth, Aaron Lennon, Jose Mourinho, Tom Huddlestone, Michael Dawson, Peter Crouch, Roman Pavlyuchenko, Dean Whitehead, Younes Kaboul, Luka Modric, Gareth Bale Places: Madrid, Spain, United Kingdom
Source: Daily Mail
Source: Daily Mail