Republic of Ireland international striker Keane's 78th minute equaliser was Tottenham's first goal in six hours and three minutes of play. It got the White Hart Lane side out of jail as they wasted a host of chances - including Jermain Defoe missing a penalty - and were also indebted to the heroics of goalkeeper Paul Robinson.
After James Milner had marked his first appearance at Villa Park by firing David O'Leary's side into a fourth minute lead, Robinson stood firm with a heroic display.
Villa would have had the game sewn up before half-time if they could have found another way past Robinson. They were made to pay a heavy price for their failings in front of goal - especially as Keane's equaliser came only a minute after £6.5million striker Milan Baros had squandered a one-on-one with Robinson.
Villa may still be unbeaten at home this season but that is of small comfort as this was definitely two points dropped.
Tottenham had no idea of the early storm they were about to face when skipper Ledley King was inches away from heading them in front after just three minutes.
They were behind 60 seconds later and would have trailed 3-0 inside nine minutes but for Robinson.
Tottenham were punished after Jermaine Jenas gave away the ball in midfield. Baros surged clear down the left wing before squaring the ball to the unmarked Milner.
The England under-21 international winger had a quick look up before drilling a low 20-yard drive past Robinson.
Robinson may have felt he should have done better with Milner's strike but the England international did redeem himself twice in the space of two minutes with smart saves from Baros and Patrik Berger.
Having managed to survive any further damage, Tottenham were able to work their way into the game and should have drawn level after 20 minutes following the persistence of Defoe.
He won a tussle with Liam Ridgewell on the left edge of the Villa area and whipped in a cross straight to the feet of Teemu Tainio.
The Finnish international only had Thomas Sorensen to beat from six yards but fired the ball well over the bar.
Tianio's blushes should have been spared seven minutes later but this time it was Defoe who fluffed his big chance when he failed to convert from the spot.
Referee Steve Bennett adjudged that Villa's new £3.5million left-back Wilfred Bouma, who was making his home debut after his arrival from PSV Eindhoven, had handled a long throughball from Young-Pyo Lee while under pressure from Defoe.
Defoe stepped forward to take the resultant penalty but Sorensen, who had been criticised for his performance in Monday's 4-0 defeat at West Ham, dived low to his right to turn the ball away.
Tottenham's problems went from bad to worse six minutes before half-time when they lost central defender Anthony Gardner with a pulled muscle.
They badly missed the England international and Juan Pablo Angel exploited his absence twice in first-half stoppage time only to be denied on each occasion by Robinson.
But Robinson was left stranded 16 minutes into the second half only for Ridgewell's volley from Berger's free-kick to crash off the bar.
Amazingly, Defoe struck the woodwork himself less than a minute later after latching on to a flick from Grzegorz Rasiak and outpacing Olof Mellberg as Tottenham's lack of success in front of goal looked set to continue.
But the introduction of Keane in the 67th minute turned the game in Tottenham's favour. Villa struggled to cope with his trickery and, after the ball ran loose following a run into the box by Defoe, Keane surged forward to fire his shot past Sorensen from 12 yards.
MAN OF THE MATCH: Paul Robinson (Tottenham) - Villa would have been out of sight before half-time but for the England international who once again continued to enhance his reputation with a stunning display.