The hosts took the lead through Grant Ward 27 seconds into the second half but Barnsley captain Conor Hourihane levelled within four minutes.
Ipswich then netted twice in three minutes as Ward got a second and David McGoldrick netted a penalty. Marley Watkins pulled one back but Ward completed his hat-trick late on.
Paul Heckingbottom started seven of his play-off final heroes along with fit-again Aidy White as well as new signings Andy Yiadom, Ryan Kent and Tom Bradshaw.
The Reds did not get off to an ideal start as last season's top-scorer Sam Winnall limped off clutching his hamstring after just four minutes and was replaced by Watkins.
Ipswich were on top early on as Daryl Murphy was put clean through but was denied by an outstanding last-ditch Marc Roberts tackle then Bradshaw blocked Teddy Bishop's goal-bound shot with his chest after goalkeeper Adam Davies flapped at a corner.
Kevin Bru also shot wide from 20 yards while the home fans and players wanted a penalty for an alleged handball by former Ipwich youngster Hourihane.
Bradshaw then missed a glorious chance for the visitors on 19 minutes when, after being picked out by an excellent Watkins cross, he put a free header straight at former Barnsley goalkeeper Bartosz Bialkowski from close range.
Adam Hammill stirred up memories of his play-off final wonder goal but this time his 25-yard effort was just wide on the top right corner. Davies made a comfortable save from a scuffed Freddie Sears shot after a swift counter-attack.
Bradshaw then missed a great chance on the stroke of half-time. After Hourihane pumped a ball back into the box following a corner and Roberts won a header, the debutant had the goal gaping in front of him eight yards out but his powerful shot was incredibly turned wide by an exceptional Bialkowski save.
The hosts took the lead straight after the restart when half-time substitute netted on his Ipswich debut with a close range finish following a move down the left.
But it was 1-1 on 50 minutes when Hourihane smashed in from close range following headers from Josh Scowen and Watkins.
Ten minutes later Ward was afforded far too much space on the right of the box after a cross was deflected into the air. The midfielder fired into the right side of Davies' net via another deflection after Barnsley defender were very slow to close him down.
Within a minute of the restart, Ipswich had a penalty as a combination of Yiadom and Roberts brought down Murphy then McGoldrick netted from the spot.
Watkins pulled one back with 15 minutes left when he headed in a Hourihane free-kick from the right wing. But Ward got his third with six to play as his shot from the edge of the area went through a crowd of bodies and nestled in the bottom right corner. Payne was denied from point blank range by Bialkowski in injury-time as Barnsley could not find a way back.
