The North London side was able to seal the points through a debut strike from the Togo international and a late Jermaine Defoe goal.
Adebayor and Scott Parker made their debuts for Spurs with the club needing fresh impetus after a poor start to the season. Tottenham entered the game at the bottom of the table and had only recorded three wins in its last 14 games.
Adebayor has now scored on his three debuts in English football for Tottenham, Manchester City and Arsenal, despite a quiet performance at the Molineux.Tottenham started the game brightly with two corners in quick succession to set the tone early. Jermaine Defoe was able to get an early effort in when the second corner was cleared by Wolves midfielder Karl Henry and Parker was able to feed in Defoe, who struck an effort wide.
Spurs continued to pressure Wolves and went even closer on the 10th minute when Luka Modric sent Benoit Assou-Ekotto down the left and his low cross was almost turned in by Wolves captain Roger Johnson. Wayne Hennessey reacted well to keep it out and Niko Kranjcar’s follow-up effort was deflected over.
Despite this early pressure from Spurs, the team was lucky not to go behind four minutes later. Jamie O’Hara, who was playing against his former club, was able to pick up the loose ball on the edge of the area, after Richard Stearman stole possession away from Kranjcar, and he unleashed a fierce drive which American keeper Brad Friedel saved.
Wolves, who have topped the table twice this season, began to take control of the game in the midfield restricting Spurs to counterattacks.
Ledley King, who has been told by Spurs manager Harry Redknapp that he has to play at least 20 games to get a new contract at the end of the season, almost gave his side the lead on the 23rd minute.
Kranjcar sent in a corner from the left and King rose highest for a free header, but he could only direct the ball into the ground, and it bounced wide.
Adebayor had his first effort on half-hour mark after Modric found him in space but his low effort from outside the area was easily saved by Hennessey. The Togo international struggled to get into the match in the first half after being marked out of the game by Stearman.
Wolves went close five minutes later as Kightly’s teasing free kick to the far post just failed to get the crucial touch by Scotland striker Steven Fletcher, and the ball whistled past Friedel’s far post.
Roger Johnson should have put the home side ahead on the 40th minute when he made a late run into the box and headed Stephen Hunt’s corner towards the goal but Modric cleared on the post.
However, both teams were guilty of spurning chances as on the stroke of halftime. Defoe stole the ball from O’Hara, drove towards the goal and his low shot was brilliantly palmed away by the keeper Hennessey for a corner.
After the break, both teams had half-chances with Adebayor and Doyle both testing the keepers, but the tie was mainly played in midfield with Henry and Parker becoming embroiled in a heated midfield battle.
However, 20 minutes into the second half, the crucial breakthrough came due to an Adebayor goal. It was Parker who set him up with a wonderful ball through to the former Arsenal man, who nipped around Hennessey and slotted the ball home.
This sparked the game into life and soon after O’Hara whipped in a cross which should have been met by a Wolves head, but instead it rolled out for a goal kick.
Not soon after, Fletcher stormed forward into the area but was tracked all the way by Parker, so he could only send a tame shot wide of the left hand post. Parker was enjoying an influential debut and he would also have a part to play in Spurs’ second.
With 10 minutes to go, the England international fed Kranjcar, who was able to send the ball towards Defoe and he finished well from close range with a low shot to seal Redknapp’s first three points of the season.
Despite a late flurry of substitutions, Wolves have suffered their first loss of the season after struggling to find a way past the Spurs backline.