Olof Mellberg, who could be on the verge of agreeing a move to Italy later in the year, gave Villa a 41st minute lead only for Jermain Defoe to put the game back into the melting pot with his equaliser 11 minutes from time.
It was then that Laursen, who missed a glorious goalscoring opportunity in the first half, headed home skipper Gareth Barry's right-wing corner in the 85th minute to enable Villa to snatch a dramatic win.
In front of another full house, Villa were the better team for much of the early play but then tailed off only to stage a late rally to win their second game in the space of four days.
Spurs were disappointing and only came to life in the second half when forced to chase the game when Robbie Keane made a major impact.
Dimitar Berbatov, the highly-rated Spurs striker, who is attracting ever increasing interest from the likes of Manchester United and Chelsea, was a big disappointment and hardly made any impact as he went into the January sales window.
Luke Moore, who last started for Villa on November 3 in the 2-0 win over Derby, could have made a story-book return in only the fifth minute.
Stiliyan Petrov, also recalled, played a pass inside to Moore who shot on the turn only to see the ball go the wrong side of the post.
But Villa conspired to make life difficult for themselves as highlighted in the 24th minute. A shot was blocked and it rolled out to Laursen who somehow managed to balloon his shot over the bar from about eight yards.
At this stage there was little likelihood of the eight-goal thriller involving the two teams a few weeks ago. Spurs, in fact, were very casual and posed little or no threat whereas Villa were persistently hammering away in their search for the lead.
This persistent attacking play finally earned Villa their just reward in the 41st minute. Kevin-Prince Boateng conceded a foul on Ashley Young and from the winger's cross Mellberg, who was not man-marked by Michael Dawson for the first time in the game, headed past a helpless Paul Robinson.
It was significant that it was the first time Villa had found themselves ahead at the break in their last four home games.
But they were somewhat fortunate to maintain this advantage as Berbatov had a wonderful chance to equalise only to shoot straight at Scott Carson.
In an attempt to change Spurs' options, manager Juande Ramos made three quick changes at a time when Villa appeared to losing their own composure.
Keane's introduction in particular had a major impact on Spurs. Suddenly their attack looked dangerous and only a lucky block prevented another substitute, Jamie O'Hara, grabbing the equaliser with Villa on the back foot.
It was, however, Moore who should have put the game out of Spurs' reach in the 69th minute when he jabbed the ball wide from close range to allow the visitors back into the match with Defoe's goal.
Laursen then came up trumps with his winner when he powered home his header from Gareth Barry's corner.