Free-scoring Ipswich looked to have been held to their first goalless draw in 55 matches as the game headed into stoppage time.
But Darren Bent's 18th league goal of the season put Ipswich ahead - only for Royals defender Ivar Ingimarsson to snatch a dramatic equaliser seconds later.
Bent side-footed home Darren Currie's deflected centre after the winger had pounced on a slip by Reading captain Graeme Murty.
Reading regrouped and charged forward from the kick-off, Icelandar Ingimarsson keeping his cool to smash home Glenn Little's teasing centre.
Until then, Reading's hero was goalkeeper Marcus Hahnemann, who kept his side level with a series of superb second-half saves.
The American shot-stopper thrust out a hand to flick over Bent's stinging shot midway through the half, then somehow clawed away Kuqi's header from a Daniel Karbassiyoon cross.
Town defender Richard Naylor was twice unlucky not to get on the scoresheet, first seeing a header from Currie's corner headed off the line by Nicky Shorey and then sending an overhead kick agonisingly wide.
A goal seemed certain to come - and when it did it looked an undoubted winner for top of the table Ipswich.
Murty was caught in possession and Currie's pass bounced off Ingimarsson into the path of Bent, who could hardly fail to end Hahnemann's brave resistance.
But Reading's response was remarkable, after midfielder Harper called on his team-mates to pour forward from the kick-off.
Little's resulting cross caused panic at the far post, and when the ball fell into the path of Ingimarsson he struck a sweet volley to show his forwards how it should be done – just as he had done in the dying minutes of Reading's FA Cup third round tie with Swansea.
Ipswich had started the game almost as dramatically as it was to finish, the outstanding Shefki Kuqi spotting Hahnemann off his line and looping a 30-yard volley onto the top of the relieved keeper's crossbar.
But once Reading settled they began to dictate play, though their possession rarely translated into chances as Steve Coppell's side struggled to show a cutting edge.
Little was Reading's most dangerous player and he created a chance for himself midway through the first half when he ran down the left and cut inside before driving a right-foot shot straight at keeper Kelvin Davis.
But it was Ingimarsson who emerged the hero with Reading's first league goal in 2005 to steal a point in the most dramatic of fashions.