Villa had conceded 15 and scored none in their last three matches with defeats by Chelsea, Tottenham Hotspur and modest Wigan Athletic putting manager Paul Lambert and his youthful side under major pressure.
The 1982 European Cup winners flirted with relegation last season and the sacking of Alex McLeish at the end of last term seems to have made little difference for an American-owned side who have put almost all their faith in blooding youngsters.
While their ambitions have been lauded by many in the game alarmed by big-money transfers and the advent of the "mercenary" player, the risk of being dragged into a dropzone dogfight is too much for fans of the Birmingham club to contemplate.
Lambert, though, believes they can now build on the draw and move up from 16th in the 20-team table.
"I've got a lot of faith in what we're doing and we won't deviate from it. Even after the heavy defeats we were keeping spirits up," he told the BBC.
The fluctuating nature of the game in Wales summed up the ebb and flow of the middle and lower reaches of the league where anyone can beat anyone else on a given day by any score.
Eighth-placed Swansea were completely on top in the first half with Wayne Routledge rounding the goalkeeper for the ninth-minute opener and Michu hitting the post as Villa fans feared the worst.
An equaliser came out of the blue from Austrian striker Andreas Weimann just before halftime after good work from Belgium's Christian Benteke - Villa's only big buy on the field - and they were ahead six minutes from time.
Nathan Dyer fouled Weimann and Benteke converted the spotkick only for Danny Graham to fire in from eight metres in stoppage time.
"With 30 seconds to go you expect to see it through. First half Swansea were right on top but second half we were very good," Lambert added.
"The goal before halftime did change it. We have a lot of injuries so you have to give credit to the players. It is a big point for us."
Swansea counterpart Michael Laudrup, whose stylish team have continued where they left off last term under now Liverpool boss Brendan Rodgers, could not believe the score after a flowing first-half display characterised by inspired July signing Michu.
"We could have been 4-0 up after 12 minutes. Incredible," the Dane said.
"The only negative part was conceding a goal in the end of the first half and not scoring a second one. Aston Villa really fought after three losses. They wanted to do everything to get a point and got close to getting three points. We could have lost but should have won." (Reporting by Mark Meadows, Editing by Tom Pilcher)
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