Spurs looked to be heading for defeat after Arsenal, inspired by substitute Cesc Fabregas, came from 1-0 down to lead 2-1 with just minutes to go at White Hart Lane.
But Jenas earned Tottenham an undeserved point when he fired a superb 25-yard effort past Jens Lehmann with referee Mike Dean poised to blow for full-time.
It was harsh on Arsenal who totally dominated the second half and recovered from Robbie Keane's 30th minute opener to lead through goals from Kolo Toure and Emmanuel Adebayor.
But Tottenham will be celebrating long and hard after their late, late show.
They started the game strongly and almost opened the scoring after three minutes when Dimitar Berbatov hassled William Gallas into a mistake and the Frenchman's header fell for Keane, who couldn't quite find the net.
And, after Arsenal had an Adebayor effort disallowed for offside, the home side took the lead after half an hour from a well-worked corner routine.
The kick was delayed first as Arsenal keeper Lehmann grappled with Berbatov, appearing to elbow him in the chest as the Tottenham striker made a nuisance of himself in the six-yard box.
Referee Dean chose to book Lehmann, Berbatov and Arsenal midfielder Abou Diaby for the incident and the episode was enough to cause the Gunners to lose concentration when the corner was re-taken.
Tottenham took full advantage with Jenas sending over an out-swinging kick that Michael Dawson met with a downward header and Keane diverted into the net.
It all looked set for a dramatic Spurs victory but Fabregas changed all that.
The Spaniard produced a stunning reverse pass with almost his first touch to set up Emmanuel Eboue, whose low drilled shot came back off the post and Adebayor blasted the rebound over the bar.
Arsenal's revival continued after the break when Toure's header cannoned back off the bar and Tomas Rosicky had a shot well saved by Paul Robinson.
Then, amazingly, they struck the woodwork again when Adebayor's header looped on to the crossbar after 59 minutes.
But the inevitable goal came eventually after 64 minutes when Fabregas swung in a deep free-kick from the left and Toure somehow forced home a deflected shot at the far post.
The Gunners then went all out for a winner with Gilberto Silva drilling an effort just wide and Eboue sending over a wonderful low cross that was just missed by Adebayor.
And they got their reward when, from another Fabregas free-kick, Adebayor rose majestically at the far post to head high into the net.
But it was Tottenham who had the last word four minutes into injury time through Jenas' pinpoint low strike which found the bottom corner of the net past the diving Lehmann.