But with both defences taking an afternoon off, the Swans drew level for a second time.
With six goals in his last ten games, Gylfi Sigurdsson was left criminally unmarked as Barrow turned provider, his strike sailing into the roof of the net.
But there was one last twist – the Swans going to sleep again at a short corner, Steve Cook planting his 78th-minute header beyond the hapless Lukasz Fabianski.
Swans’ first-team coach Alan Curtis was disappointed to return to south Wales empty handed.
He said: “It’s going to be hard between now and the end of the season.
“I’m really disappointed – we clawed ourselves back into the game twice but due to individual errors and mistakes, we lost.”