Strikes from Keane, who started his career as a trainee with Wolves, and Jermain Defoe ended a run of six successive away defeats for Spurs.
But Wolves, beaten for the first time in five games, should have been out of sight before Keane opened the scoring with his 16th goal of the season.
To add to their misery, Wolves had to play the final 23 minutes of the match with ten-men after the dismissal of skipper Paul Ince.
It was also a disappointing end to his career for Wolves defender Denis Irwin, 38, who was making the 902nd and final appearance of his career.
Tottenham were fortunate not to be trailing by four goals before Keane struck against the run of play.
Twice goalkeeper Kasey Keller saved them while the woodwork also came to their rescue on two occasions.
Keller pulled off smart saves in the opening two minutes from Paul Ince and Henri Camara.
Carl Cort rattled the cross bar with a 12th minute header before Irwin hit the foot of the post with a 25-yard free-kick in the 17th minute.
It took Spurs fully 30 minutes to mount an attack and when they did, Wolves goalkeeper Paul Jones had to tip a rising drive from Rohan Ricketts over the bar.
It was a warning that the home side failed to heed and they paid the price when Republic of Ireland international striker Keane struck.
He was picked out by a cross from Mark Yeates and was faced with just Jones to beat. The Welsh international managed to save Keane's first shot but the rebound fell kindly for the Irishman who steered his shot home off the far post.
The strike effectively ended Wolves' challenge and they never again posed the threat that they had carried in the opening stages.
They then effectively handed Tottenham all three points when Cort gifted Defoe the decisive second goal in the 57th minute. His weakly hit back-pass was intercepted by Defoe who waltzed around Jones before firing the ball into an empty net to grab his seventh goal for the club since his arrival from West Ham United.
Wolves' misery was completed ten minutes later when Ince, who had been booked for diving in the first-half, was dismissed by referee Steve Bennett for a rash challenge on Tottenham skipper Jamie Redknapp.