A feisty derby was, for the most part, high on passion but low on quality as the points were shared in North London.
An action-packed first half failed to produce a breakthrough, but conspired to throw up everything but.
Eboue had the ball in the net inside 15 minutes but saw his effort chalked off for an earlier infringement by Emmanuel Adebayor.
Arsenal's talismanic Togolese striker was then stretchered off after pulling up with a hamstring problem, before Eboue saw red for a second yellow card.
The Ivorian was cautioned for dissent after 17 minutes and was handed his marching orders 20 minutes later after tangling with Luka Modric.
The hosts did look lively on the occasions they ventured forward but Aaron Lennon and Roman Pavlyuchenko wasted the better of their opportunities.
Chances continued to come and go for Harry Redknapp's men after the break, with Pavlyuchenko blazing over when well placed and Robbie Keane glancing a header onto the top of the netting as Manuel Almunia found himself stranded in no man's land.
Arsenal's ten men began to tire as the game drew on, but Alexandre Song did have a glorious opportunity to steal the points on 70 minutes when he diverted a volley the wrong side of the post from eight-yards out.
Tottenham finished the game well on top but were ultimately unable to turn their mounting pressure into a match-winning goal.
TrippedIt was the home side who started brightly, forcing a couple of early corners.
Keane, making his second debut for Spurs, went down under the challenge of William Gallas on the right side of the penalty area, but referee Mike Dean was having none of it and waved play on.
Robin van Persie and Eboue combined down the Arsenal right to release the Ivory Coast winger, but his centre across goal from a tight angle was just too far ahead of Adebayor.
Eboue was in again after 13 minutes when he scampered into the left side of the Spurs box, but was crowded out.
However, he then tripped Jonathan Woodgate before regaining the loose ball and stabbing it into the net, with celebrations cut swiftly short by the referee's whistle.
Bacary Sagna got clear on the overlap down the right, but his cross was not deep enough and easily cut out at the near post with red shirts waiting in the middle.
Eboue picked up a needless caution, but one which would later prove so costly, for complaining at the award of a free-kick against Sagna on Modric after 17 minutes.
On the half-hour, Croatian Modric created space for a shot from the edge of the penalty area, and Almunia had to make a smart save low to his right.
Gael Clichy chased what looked like a lost cause down the left with Vedran Corluka, Samir Nasri nicked the ball from on the goalline before the full-back sent a low pass across the face of goal, which just eluded Adebayor.
That proved to be the last action for the African, who pulled up mid-run and was eventually carried off on a stretcher around the perimeter.
AdvantageBefore Arsenal could make a change, they were down to 10 men.
Modric and Eboue clashed on the near touchline and the referee had seen enough to caution both men - showing Eboue, who kicked out to trip the Spurs man, a second yellow card followed by a red.
Once calm had been restored, Nicklas Bendtner replaced Adebayor in the 38th minute.
Spurs looked to make their advantage count before the break and in stoppage-time Almunia tipped over a fierce 20-yard effort from £14million-man Wilson Palacios.
At the start of the second half, Pavlyuchenko capitalised on an error by Kolo Toure to get clear into the left side of the Arsenal penalty area, but then made a complete hash of his shot which skewed wide.
After 56 minutes, Spurs came within inches of taking the lead when Keane got up to meet Lennon's cross from the right, but his close-range header skimmed the top of the crossbar.
With 20 minutes left, Arsenal had a great chance to snatch the lead when Van Persie's corner fell to Song in the six-yard box - but the midfielder could only hook the ball wide.
There was a hold-up when Clichy received treatment for a cut following a clash of heads with Darren Bent and was replaced by Kieran Gibbs.
Both sides pressed during four minutes of stoppage-time, with Carlo Cudicini tipping over from Bendtner and Almunia denying Modric.
1st Half Goals
Shots on Target
Shots off Target