The Iron were 2-0 down after 72 minutes, but goals from top scorer Gary Hooper and Matty Sparrow - in the 81st and 89th minutes - salvaged a vital point. The result also ended any lingering hopes Reading may have had of gate-crashing the play-offs with a late charge.
The game burst to life after a goalless first half in which Gyfil Sigurdsson had missed a great chance for the visitors.
Scunthorpe brushed the woodwork either side of half-time through efforts from Martyn Woolford and Grant McCann, before Hooper then produced the miss of the match when he shot wide with the goal at his mercy.
Reading made the most of that let-off when they took the lead after 48 minutes when centre-back Alex Pearce forced the ball home from a free-kick knocked high into the box by Brian Howard.
They looked to have the game sealed in the 72nd minute when Sigurdsson made it 2-0 from the penalty spot after Jobi McAnuff had been brought down by Cliff Byrne.
McAnuff then forced a terrific save from keeper Joe Murphy before Scunthorpe started their dramatic fightback.
Hooper made it 2-1 after 81 minutes when he thumped home the rebound after a shot from Garry Thompson had only been half-blocked by keeper Adam Federici.
Then, just a minute from the end of normal time, midfielder Sparrow crashed home an equaliser after substitute Jonathan Forte had nodded the ball down in the box.