Ipswich, who had led 2-0 at the break through goals from Gary Roberts and George O'Callaghan, simply raised their level and netted three more through Danny Haynes and Francis Jeffers before Jon Walters sealed the rout in stoppage time.
Barnsley's bid to stay up suffered the worst possible start when Town went ahead on two minutes with Jaime Peters crossing for Roberts to net from 12 yards.
Walters shot narrowly wide for Town before a Kyel Reid-led break should have brought a Barnsley equaliser but their own players got in each other's way before Brian Howard blazed over.
Lewis Price pulled off a fine diving save to deny Ritchie Jones' low 20-yarder before Walters and Alan Lee worked a neat one-two with Walters freeing Lee who crashed a shot against the crossbar.
Nick Colgan made a superb save to deny Owen Garvan after neat interplay with Walters and twice denied Lee efforts, but he was helpless on 43 minutes when O'Callaghan collected a loose ball 20 yards out and drove his first Ipswich goal into the corner.
Ipswich continued to dominate after the break and even had the luxury of replacing top-scorer Lee with former England forward Jeffers.
However, they squandered numerous chances to extend their lead and suddenly the game was back in the balance when Nardiello curled a superb 30-yard free-kick past Price on 79 minutes.
Almost immediately, Haynes saw an angled shot blocked by Colgan when he should have squared to the unmarked Jeffers and Walters, but he soon atoned by spinning to fire home after Jeffers had a shot blocked.
Barnsley's spirit was broken and Town rubbed salt in the wounds with two more goals in the last four minutes as first Garvan and Walters set up an unmarked Jeffers to slot beyond Colgan.
The cherry on top of the icing for Ipswich came in stoppage time when Haynes fed Jeffers whose drive cannoned back off the bar but Walters was on hand to fire in the rebound.
For Barnsley, things are beginning to look desperate and they don't get any easier with Birmingham set to visit Oakwell on Monday, while a relaxed Ipswich head to Hillsborough to face Sheffield Wednesday.