The high-flying Tractor Boys were totally outplayed in the opening 45 minutes and fell behind to David Mirfin's looping header on the half hour.
But substitute Jaime Peters grabbed a fortuitous equaliser 12 minutes into the second half and Ipswich then saw several chances go begging as they piled forward in search of a winner.
Scunthorpe also threatened to register a second goal in an enthralling finish to the match, but both sides had to settle for a point.
Ian Baraclough made two changes to the Scunthorpe side beaten 5-2 by Manchester United in the Carling Cup on Wednesday, with Michael Collins and Rob Jones coming in for Michael O'Connor and Niall Canavan.
Ipswich boss Roy Keane reverted back to the team that defeated Cardiff 2-0 in their last league outing. New loan signing Jake Livermore was named among the substitutes.
The visitors struggled to establish a foothold in the game early on as Scunthorpe dominated possession.
Martyn Woolford and the returning Jones both went close for the Iron before Jonathan Forte spurned the first clear-cut opportunity in the 15th minute.
Eddie Nolan's left-wing cross picked out the striker at the far post, but he headed over from eight yards.
Scunthorpe went close again five minutes later as Jones beat Town goalkeeper Marton Fulop to a Josh Wright corner and headed narrowly wide.
The hosts were eventually rewarded for their pressure after 30 minutes. Sam Togwell lifted a long ball back into the area after a corner had been cleared and Mirfin was left unmarked to nod a looping header over Fulop.
Keane was clearly unimpressed by his side's showing and immediately hauled off highly-rated teenage forward Connor Wickham, with midfielder Luke Hyam coming on in his place.
The Tractor Boys did finally threaten in the 36th minute as Jason Scotland just failed to connect with a cross from Carlos Edwards.
Jones was also called upon to block a shot from Gareth McAuley as Edwards bombarded the home defence with a succession of long throws towards the end of the half.
Keane made another change at the break, replacing the ineffective Andros Townsend with Peters.
And the substitute took just 12 minutes to make an impact as he grabbed a barely deserved leveller for the visitors.
Cliff Byrne's attempted interception ricocheted off Peters and the winger was left with a simple finish from 12 yards.
The goal roused Ipswich into life and they wasted several chances to take the lead in a frantic five-minute spell.
Murphy made a fine stop to deny Edwards after the former Sunderland man had been played clear through on goal. Scotland appeared certain to tap home the rebound only for Cliff Byrne to deny him with a superb last-ditch tackle.
David Norris forced Murphy into further action moments later and Darren O'Dea saw a shot rebound off the crossbar after the Scunthorpe keeper had flapped at another throw from Edwards.
The hosts had another let-off with 14 minutes remaining as Jones cleared a Peters header off the line before seeing substitute Tamas Priskin nod over the bar.
Scunthorpe had chances of their own in the closing stages and Forte was superbly denied by a combination of McAuley's challenge and Fulop's fingertip save.
Forte then wasted an even better opportunity with four minutes remaining as he dragged a left-footed shot wide from the edge of the area after leaving two Ipswich defenders trailing in his wake.