Rangers looked like claiming a second 2-1 win against Town this term after goals from Stefan Moore and Paul Furlong either side of a Jason De Vos header, only for Danny Haynes to nod home in stoppage time.
Haynes was the second 17-year-old Ipswich turned to on the day to make home debuts, after striker Billy Clarke enjoyed a lively first-half performance, before being surprisingly withdrawn.
The game started on a sour note when Furlong unnecessarily followed in a free-kick and caught Town keeper Lewis Price on the head and was fortunate to only see a yellow card from ref Matt Messias.
Early on there was little in the way of goalmouth action, with Town coming closest when a Darren Currie corner curled right across goal, then from a QPR free-kick, Richard Langley's delivery was nodded wide by an unmarked Danny Shittu.
After a quiet spell, the game burst into life with three goals in 16 minutes - the first when Moore played the ball wide to Gareth Ainsworth, then raced into the middle to nod home the cross.
That brought Town to life and Jimmy Juan saw one goalbound effort deflected over and then Furlong nodded his header off the line, before Simon Royce dived to keep out a Richard Naylor header.
Town's pressure resulted in a deserved equaliser on 33 minutes when De Vos steamed in to head home another pinpoint Currie delivery for his first goal of the season.
The home side were on top, but conceded again on 42 minutes when Ainsworth beat Fabian Wilnis to the byline, and his cross then deflected to loop over Price's head and present Furlong with a chance to force the ball home, holding off Sito Castro at the far post.
Price did well to punch away a Langley free-kick after the break and then Furlong did well back in his own area to clear as Juan looked poised to sweep in a De Vos flick-on from a long throw.
Naylor headed a driven Currie corner wide, as Town continued to only really carry a threat from set plays, while QPR were happy to play on the break, with Moore shooting wide from a Furlong flick.
Half-time sub Ian Westlake drilled across the area as the game entered its last ten minutes, with Ipswich looking increasingly unlikely to find a way through, despite using all three subs.
Matt Richards blazed a 25-yard half-volley over as Rangers were content to get bodies behind the ball, and then another sub, Haynes, got his head on a Currie cross, and although he got the power, his effort sailed over.
Naylor sent a looping header sailing comfortably into the arms of Royce, but then, as the game entered the first of four added minutes, Haynes rescued a point with his first senior goal.
The youngster darted in off the right wing to get between Mauro Milanese and Ian Evatt and guided a neat header beyond Royce's right hand after racing on to an intelligent floated ball from another Town sub Jim Magilton.
Neither side created another clear opening after that and in the end a share of the spoils was about right.