Although the hosts will be disappointed to see the run ended, this was their fourth successive clean sheet at fortress Portman Road and they now have not conceded a goal in almost seven hours of football at home.
Barnsley made a lively start and should really have scored on 12 minutes when Sam Togwell found himself unmarked at the far post from a Grant McCann cross but missed his kick eight yards out.
Istvan Ferenczi shot wide on the turn moments later before Ipswich threatened for the first time on 19 minutes when Alan Lee's cross was volleyed firmly by Gavin Williams but straight at Heinz Muller.
Pablo Counago forced a diving save from Muller after a neat turn onto a Billy Clarke pass and then Town keeper Neil Alexander acrobatically tipped over a fierce 30-yarder from McCann.
From the corner, taken by McCann, Stephen Foster got a floated header in but Alexander grabbed it fairly easily before Town suffered a blow on 33 minutes when joint top scorer Lee went off with a stomach bug.
Clarke shot over as Ipswich tried to build a head of steam up as half-time approached, with Jon Walters shooting straight at Muller on the turn and then sub Danny Haynes firing wide from a Counago pull-back.
Ipswich twice came close early in the second half to getting Tommy Miller in on balls through the centre of the Barnsley rearguard, but each time the visitors just managed to scrape the ball away.
A mistake by Dan Harding let in Togwell at the other end but, although he clipped the ball past the advancing Alexander, it went across goal with no team-mate in position to finish off his good work.
The save of the game came on 66 minutes when sub Gary Roberts was fouled 25 yards out. Williams' curling free-kick was heading into the top corner before Muller flung himself to turn it over the bar.
Haynes blazed a volley over from a Williams cross after the resulting corner was only half-cleared, before both Counago and Walters had attempted back-heels from close range blocked by covering defenders.
For most of the half Barnsley had been concentrating on keeping things tight, but at times they threatened on the break with McCann and Anderson both off target from distance and an ambitious Dominic Werling 40-yarder forced Alexander to turn the ball behind for a corner.
Foster and Anderson were booked in the final ten minutes as Ipswich desperately searched for a winner, with the best chances being a blocked Roberts shot and a header wide from a Williams corner by skipper Jason De Vos.
So, Ipswich's run of successive home wins ends three short of the mark set by Sir Bobby Robson's 1980-81 team, two members of which - Mick Mills and Kevin Beattie - were watching from the press box.