Lee Trundle's return to Brian Flynn's side proved as vital as ever as his last-ditch goal saved the Swans once more.
Trundle blasted home the winner just seconds from time after the Swans looked to have thrown away a two-goal lead.
Trundle had put the hosts in the driving seat with a 29th minute penalty, a Gavin Williams trip on Andy Robinson giving the top scorer the easiest of chances to reopen his account.
And the bumper 9,800 Vetch Field crowd thought the points were all theirs when Karl Connolly, making his first home appearance since breaking his ankle against Huddersfield in September, slotted home from a 66th minute corner.
But Yeovil refused to lie down and Williams made up for his earlier error when he beat Roger Freestone from inside the area in the 73rd minute.
And Yeovil eventually found the leveller they were so desperately searching for when Wales Under-21 star Kevin Gall pounced in the 89th minute to break the hearts of his fellow countrymen.
But Glovers boss Gary Johnson had to cut short his celebrations when Trundle struck just moments later, the lethal Liverpudlian lashing home the ball after Brad Maylett and Robinson had caused havoc in the visitors area.
And Swans boss Brian Flynn could not hide his delight at the dramatic victory which pushes his side back in the promotion frame.
"This result shows that on our day we are a top three side," he said. "It was probably our biggest win of the season and I'm delighted at the way we came back.
"We've only beaten one other top-six side and we have to beat them if we are to have any chance of proving we're the best.
"It was the best we've played since the start of the season but we're in the middle of a tough period and the next two games are just as important.
"It shows how vital Lee Trundle is to us. He brings a feel-good factor to the whole team when he plays and even the crowd because he's so skilful, so sharp and is a born winner."