Ciaran Clark's deflected shot gave Villa a half-time lead and then the visitors had defender Danny Rose sent off early in the second half for a challenge on ex-Spurs player Alan Hutton.
Emmanuel Adebayor levelled from the penalty spot for Harry Redknapp's side but they are now a point behind third-placed Arsenal going into the final weekend of the campaign.
Villa equalled the Premier League record of 17 draws in a campaign held by themselves in 2006-2007 and Newcastle in 2003-2004.
But it means Alex McLeish's side have ended the season with only four home wins - the least number in a season in their history - and fans chanted "sack McLeish" at the final whistle.
Tottenham will be kicking themselves for failing to take advantage of Arsenal's home draw with Norwich.
They now must hope their north London rivals slip up at West Brom to keep alive hopes of a top-three finish.
McLeish again opted to remain seated in the dug-out - a policy he also adopted at West Brom last weekend - with Peter Grant handing out instructions to players.
Charles N'Zogbia had the first attempt on goal after good play by Emile Heskey but his shot was deflected over the crossbar of former Villa goalkeeper Brad Friedel.
Adebayor found a yard of space inside the Villa box but his effort from a narrow angle flew wide of the far post.
Heskey should have done better when found in space by Stephen Ireland but he hesitated before shooting and Younes Kaboul was able to make the challenge.
Gareth Bale showed his pace for the first time after 16 minutes and forced his way into the Villa box but he was stopped in his tracks by Richard Dunne's challenge.
Kaboul became the first player to be yellow carded for bringing down Heskey.
Tottenham were dominating possession and Bale headed wide at the far post under pressure from Hutton after good play by Rafael van der Vaart and Aaron Lennon.
But after 35 minutes a deflected shot from Clark gave Villa the lead against the run of play.
The Republic of Ireland midfielder was 30 yards out and his shot hit the shoulder of Gallas and flew past the stranded Friedel into the net.
Tottenham tried to retaliate and Given turned a fierce drive from Bale around the post.
After 49 minutes Spurs were reduced to 10 men when left-back Rose was given a straight red card for a lunge at Hutton right in front of the dug-out.
Redknapp was incensed by the decision and there was also words exchanged between McLeish and Spurs coach Joe Jordan.
Hutton limped out of the action to be replaced by James Collins and at the same juncture Heskey, who had picked up a first-half knock, made way for Andreas Weimann.
Adebayor tried to take advantage of a quick free-kick and skipped past Dunne to find himself with only Given to beat. But he tried to side-foot his shot into the corner of the net and did not extend the Republic of Ireland keeper.
Spurs still looked the more dangerous and after an hour Adebayor brought them level from the penalty spot.
Dunne was adjudged to have brought down Sandro and was yellow-carded before Adebayor sent Given the wrong way from the spot for his 17th goal of the campaign.
Friedel had to react quickly in racing out of his area to hack the ball clear from Weimann who suffered a knock to his knee. He was unable to continue and was replaced by Nathan Delfouneso.
Dunne had a header blocked by Kaboul from an N'Zogbia corner in a rare Villa attack, while Bale showed good skill in the Villa box but his shot on the turn flew straight at Given.