The North London derby remained goalless at the interval, but Nacer Chadli fired Spurs into a second-half lead which was cancelled out by Alex Oxlade-Chamberlain soon after to ensure that the points were shared at the Emirates Stadium.
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Despite a flowing start to the game, it took until the 21st minute before either goalkeeper was called into action, when Danny Welbeck cut inside before drilling a shot which was well handled by Hugo Lloris.
Oxlade-Chamberlain proved to be a menace in the early stages and he almost caught Lloris out shortly after, only for the Frenchman to recover to spare his blushes.
Jack Wilshere was his usual busy self in the centre of the park and he was the next Arsenal player to test Lloris, but the midfielder's shot was straight at the Spurs stopper.
A few minutes later, there were worrying signs for the Arsenal fans as Wilshere's ankle buckled beneath him, but the 22-year-old soon returned to the field.
The game gathered pace as it approached half time, and Oxlade-Chamberlain stung the hands of Lloris once more before Chadli and then Adebayor both snatched at one-on-one chances.
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The second half began in an equally frantic fashion, with Wilshere slipping in Mesut Ozil for the first big chance. The Germany international took a touch before forcing a good stop out of Lloris low down.
Lloris was needed once more to deny the Gunners when he brilliantly kept out Per Mertesacker's header, while home shouts for a penalty were turned down moments later when Kyle Naughton appeared to handle the ball inside the box.
It looked as though it was going to a frustrating evening for Arsene Wenger's men, but Oxlade-Chamberlain emphatically finished on 74 minutes to level the game up, finding the top corner after Welbeck missed the initial effort completely.
Both sides pushed forward in the final 15 minutes in search of a winner, but it was not to be with the game ending all square.
As a result, Arsenal find themselves in fourth place in the league table, while Spurs are down in eighth.