Tottenham new boy Emmanuel Adebayor opened his Spurs account on his debut as the club got their league campaign up and running.
The Togolese forward got onto the end of fellow debutant Scott Parkers through ball before calmly rounding Wayne Hennessy and slotting home into an empty net.
Redknapp made 5 changes from the side that lost 5-1 to Manchester City bringing in Ledley King, Parker, Adebayor, Jermain Defoe and Kyle Walker all coming in for Michael Dawson, Aaron Lennon, Vedran Corluka, Rafael Van der Vaart and the recently departed Peter Crouch.
And it was Parker who almost got Spurs up and running, his perfectly executed challenge at the expense of Kyle Henry released Defoe who saw his effort deflected wide.
Adebayor could have broken the deadlock minutes later but his effort was somehow turned over the bar by Wolves' Richard Stearman after some good work from Benoit Assou-Ekotto and Niko Kranjcar.
At the other end, former Spur Jamie O'Hara saw his effort sting the palms of Brad Friedel while a Kranjcar free-kick caught the Wolves defence off-guard but the back four were alert enough to deflect any danger away from the net.
It was Wolves who created the best opportunity after 36 minutes as Michael Kightly's floated free-kick to the far post should have need headed home by Roger Johnson or Steven Fletcher.
Just before the break, O'Hara was caught in possession by Defoe who saw his effort palmed away by Hennessy while Gareth Bale hit the side netting after breaking free down the right.
After the break, new boy Adebayor almost capitalised on a loose ball but was beaten to it by Hennessy meanwhile Friedel kept O'Hara out at the other end, saving well after the former Tottenham man struck a well placed shot from the edge of the area.
After 58 minutes, Defoe capitalised on some sloppy Wolves play before playing in Adebayor but the 27-year was knocked off his stride before he chance to connect with the ball before Kranjcar failed to test Hennessy.
The breakthrough came after 67 minutes as a brilliant moment of movement and vision saw Adebayor grab his first in a Spurs shirt. Kranjcar elegantly broke forward, playing the lively Parker whose pass found the former Arsenal striker before he rounded Hennessy and put the ball into the back of an empty net.
The lead was doubled 13 minutes later as Defoe and Kranjcar linked up sublimely before the England striker fired low past Hennessy.
There was even enough time for Giovani Dos Santos to make his first Spurs appearance in almost a year as the pint-sized Mexican replaced Defoe in the 87th minute.
A 2-0 win was a welcome result to the Spurs faithful with many expecting a draw, at best, leading into the fixture after losing to Manchester United and City in the opening two Premership encounters, conceding eight goals in the process.
A welcome return for King can be considered the catalyst for a clean-sheet, with the defence looking more confident and assured this afternoon than the previous two encounters.
"This is a difficult place to come and we worked hard to get a win, but it was a deserved win," Redknapp said after the game
"It is nice to see them both (strikers Adebayor and Defoe) get on the scoresheet and it is a great start for them. It is a good and positive result for us today as this is a difficult place to come.
"I am delighted with (Adebayor's) performance and also with Scott Parker's.
"He had a good game in the midfield today, patrolled the midfield for us, broke up attacks and played up front as well.
"I am glad that the two debutants combined for the first goal but we must not forget that Brad Friedel made a good world-class save in the first half when it was still 0-0."