The Swans showed five changes from the side that earned their first league victory of the season at Coventry .
On the bench was new signing Besian Idrizaj, while visitors Scunthorpe also rang the changes after their 4-0 defeat at Sheffield Wednesday.
The Swans made the early running with Nathan Dyer using the right flank to good effect, but it was the Iron who went ahead after 14 minutes.
Paul Hayes was worked through the Swans defence but David Cornell beat his shot behind for a corner.
When Josh Wright's near-post flag kick came over, it was Niall Canavan who headed into the net with Cornell stranded on his line.
The Swans tried to hit back and Kerry Morgan and Jordi Lopez both let fly with long-range shots but they failed to trouble Iron skipper Joe Murphy.
On the half hour, Cornell went down low to push behind a goalbound shot from Martyn Woolford.
Stephen Dobbie replaced Chad Bond for the start of the second half as the Swans looked to get back on terms and within four minutes he rolled a shot inches wide with Murphy well beaten.
The change made a difference and Scunthorpe were forced on the defensive for long periods.
Dyer and Dobbie went close but, even though the visitors kept giving the ball away, the Swans were unable to make their second-half superiority count.
Idrisaj made his bow in the 76th minute but it was Dobbie who levelled the score two minutes later with a rasping shot that beat Murphy all ends up
Skipper Garry Monk was sent off in the 83rd minute for an alleged head butt on Michael O'Connor but the Swans held out for extra time.
In the 97th minute Dobbie was kicked in the stomach and forced off to leave the Swans battling with nine men.
Scunthorpe were awarded a penalty in the 109th minute after Alan Tate handled a Hayes shot and Gary Hooper dispatched the spot-kick to give his side the lead.
Gorka Pintado was the second Swan to be sent off in the 116th minute for a dangerous tackle and he was followed one minute later by Angel Rangel for use of an elbow.
The match finished in farcical conditions with Idrisaj also injured and taking no part in the game.