The Yorkshire side, who saw Jamal Campbell-Ryce dismissed for a second yellow card early in the second half, also had Martin Devaney carried off after twice taking the lead.
They thought their workrate had seen them to a fifth away draw when Byfield was sent on for the last five minutes.
With his first touch he picked up one of the eight cards issued by referee Keith Hill. With his last he prodded home a Michael McIndoe free-kick.
It was always a niggly, physical game to keep Hill busy, but exploded with four goals in 11 minutes late in the first half.
Barnsley scored the first of them just after half an hour when Devaney robbed right-back Bradley Orr to square a path to Jon Macken, whose low drive caught keeper Adriano Basso with his reflexes down.
That goal had come after a long spell of home pressure with Barnsley's keeper Heinz Muller making one great save from Ivan Sproule while City passed up two or three good scoring chances.
After scoring only once in five games, the Yorkshiremen were still in celebratory mode when City hit back within two minutes.
Their outstanding skipper Louis Carey, who had gone up for a corner, saw his header blocked, but Enoch Showunmi swooped to boot home the equaliser with his left.
Quickly Dennis Souza headed his side back in front from an inswinging corner by Brian Howard.
Then Showunmi, who had started only his fifth game this season, again rose to the rescue with a close-in header from Michael McIndoe's lob.
When they had a one-man advantage City threw everything into attack down both flanks, but it took Byfield's late intervention to bring them three Championship points.