Rose, 19, a late substitute for Jacob Mellis in the Championship clash at Portman Road, had only been on the pitch for four minutes when he headed home defender Tom Kennedy's pinpoint cross for the first league goal of his career to cancel out Luke Chambers' opener early in the second half.
Ipswich boss Mick McCarthy must have thought his side were set for their third league win in seven, but they did not deserve to be in front against his hometown club as Barnsley squandered a hatful of chances, striker Marlon Harewood in particular, in David Flitcroft's first game as permanent manager.
Carlos Edwards forced Barnsley goalkeeper Luke Steele into a flying save with a 25-yard shot in the second minute and Ipswich midfielder Guirane N'Daw headed Lee Martin's corner over the crossbar.
The visitors were dealt a blow in the 12th minute when midfielder Stephen Dawson landed awkwardly under Luke Hyam's challenge and received lengthy treatment before being carried off on a stretcher and replaced by Kelvin Etuhu.
But the setback appeared to galvanise Barnsley. Stephen Foster headed Mellis' corner over and Chris Dagnall twice went close, his angled shot blocked by Ipswich defender Chambers and then home goalkeeper Scott Loach parrying a goalbound effort.
Ipswich striker David McGoldrick's 25-yard shot was blocked, but Mellis, from similar distance, and Harewood went close again - the latter dragging his shot wide when well placed on the left edge of the area.
Chambers' brilliant tackle denied Dagnall a shot on goal when sent clear by Mellis' superb through-ball as Barnsley continued to create chances.
The best of those fell again to Harewood in time added on at the end of the first half when he fired against the foot of the post after being played in by Mellis.
Ipswich took the lead against the run of play in the 56th minute. Defender Aaron Cresswell swung the ball into the area and when Barnsley failed to clear the danger, Chambers - who had blazed a similar chance over the crossbar in the first half - lashed the bouncing ball into the bottom corner.
Chances at either end dried up as temperatures began to drop before McGoldrick's 25-yard effort drifted wide in the 66th minute.
Harewood wasted another chance when free inside the area 12 yards from goal soon after, pulling his low shot off target and Etuhu lofted a 30-yard shot over the crossbar.
Dagnall was next to pass up the opportunity of an equaliser for the visitors as he headed Tom Kennedy's cross wide from six yards and Harewood fired off target again after the ball had ricocheted to him inside the box.
But with the clock ticking down, substitute Rose climbed highest at the far post to head home the visitors' 89th-minute equaliser.