Dennis Bergkamp equalised two minutes from time but Blues stormed back with Heskey, who had generally had a quiet game, snatching a dramatic win out of the fire with a low right-foot shot.
It is the first time Arsenal have been beaten in the Premiership by the Midlanders but they could have few complaints as Blues' player of the season, Heskey, grabbed the vital winner.
Pandiani's goal only enhanced Blues' determination to retain his services next season - if they can agree a deal with Deportivo La Coruna.
Blues success certainly provided enough proof that there is every reason to be optimistic about their prospects in the next campaign.
Matching Arsenal for such long spells was encouraging in many aspects with Jermaine Pennant and Mario Melchiot emerging as key features of the side.
Pennant, described a few days ago by Blues boss Steve Bruce as being out of the same mould as David Beckham, obviously had something to prove against his former club.
He was certainly involved in much of the early play when most of Blues' attacking play came down the right with Melchiot playing a key role.
There was, nevertheless, a cool assurance about Arsenal, who made four changes from the side which routed Everton 7-0 in midweek.
The Premiership runners-up played with a confidence of a side which expected to win and extend their unbeaten run.
Patrick Vieira personified the attitude in Arsenal's team as he played with regal style to combat an enthusiastic Birmingham side that applied the early pressure in an attempt to break their sequence of never having scored against the Gunners in the Premiership.
Blues' attack was certainly much livelier than Arsenal's as was perceived in the 17th minute when Pandiani pulled the ball back into the path of Stephen Clemence, but the midfielder stumbled and lashed his effort over the bar.
The Blues were certainly encouraged by this spirited goal attempt and maintained the pressure on the Gunners who coolly soaked up the attacks with an air of nonchalance.
But it took some smart defending to keep out Blues when Pennant's cross was allowed to go unchecked by Heskey, but Darren Carter was just a little too slow to make contact on the edge of the six-yard box.
Arsenal's response was an effort from Robin Van Persie, but his accuracy left a lot to be desired as Birmingham resumed their adventurous attacking role to keep the Gunners on the back foot.
But Arsenal are never more dangerous when they are under-estimated by the opposition and Van Persie demonstrated this threat when he fired in the Gunners' best chance a minute before the break after the Blues defence had been opened up by Cesc Fabregas.
Early in the second half Dennis Bergkamp broke clear following a perfect pass from Van Persie, but the Dutchman was unable to display his usual clinical finishing.
Jens Lehmann demonstrated his value in Arsenal's goal with a brave save as he dashed from his goal to dive at the feet of the onrushing substitute Clinton Morrison.
But Pandiani set the game alight with a close-range goal following a corner from Pennant only for Bergkamp to equaliser in the 88th minute.
Blues, however, were not to be denied and Pandiani set up Heskey for his tenth league goal following a throw-in from Olivier Tebily.