Adebayor missed two sitters - one in each half - before Lomana LuaLua scrubbed out Thierry Henry's stunning opener to earn relegation-haunted Pompey a crucial point.
Fit-again Sol Campbell made his first appearance since going AWOL at half-time during Arsenal's 3-2 defeat at home to West Ham on February 1.
LuaLua gave the Champions League semi-finalists an early fright when he fired a speculative 30-yard shot two yards over Jens Lehmann's crossbar.
Henry sent Pompey goalkeeper Dean Kiely scrambling across his goal 15 minutes before half-time with a curling free-kick after drawing a foul from Benjani 20 yards from goal.
Jose Antonio Reyes had Harry Redknapp's relegation battlers on the back foot again soon after, firing into the side-netting after Henry had set off on a mesmerising run from the edge of the centre circle.
The Londoners finally made the pressure tell in the 37th minute when Henry opened the scoring with a stunning solo goal.
The Frenchman robbed Sean Davis midway inside the Pompey half before playing a neat one-two with Adebayor and beating Kiely with a perfectly-weighted side-footed strike from the edge of the box, which cannoned in off the inside of the left-hand post.
Adebayor should have doubled Arsenal's lead with four minutes of the half remaining when Henry rolled the ball across the six-yard box, only for his strike partner to scuff hopelessly wide with Kiely's goal at his mercy.
Adebayor wasted another gilt-edged opportunity in the 58th minute when he put a free header wide of Kiely's far post from Reyes' right-wing corner.
LuaLua made Adebayor pay for his wastefulness when he drew Pompey level in the 67th minute with a thunderous close-range header from Andres D'Alessandro's teasing free-kick.
LuaLua was immediately substituted to be replaced by former Arsenal junior Richard Hughes after landing awkwardly on his ankle while performing his extravagant back-flip goal celebration.
Kiely denied Freddie Ljungberg a winner, two minutes from the end, when he came racing out of his goal to save the Swede's close-range striker with his legs as Pompey clung on for a draw.
Campbell's evening was brought to a premature end soon after as he was forced off with blood pouring from is face after being caught on the nose by Portsmouth substitute Svetoslav Todorov.