All the luck seemed to be going against the Welshmen in the early stages as they suffered a double blow. First midfield man Alan Tate was sent off in the 15th minute for his challenge on Scunthorpe winger Cleveland Taylor.
Twelve minutes later Swansea then lost skipper Gary Monk, who was carried off with knee ligament damage after going into a challenge near the halfway line.
Swansea shook off those two setbacks to look dangerous on the break. Fallon went close to giving them the lead after 38 minutes with a header that was scrambled off the line by Scunthorpe skipper Andrew Crosby.
The visitors did snatch the lead in the third minute of first half stoppage time when Leon Knight threaded a pass into the box for winger Andy Robinson who crashed a great right -foot shot past keeper Joe Murphy from 15 yards.
After a poor first half performance Scunthorpe came storming out after the interval. They levelled on 49 minutes when skipper Crosby sent keeper Willy Gueret the wrong way from the penalty spot after winger Taylor had been brought down by full-back Tom Williams.
Scunthorpe continued to press forward and it took good saves from Gueret to keep out efforts from midfield men Ian Baraclough and Matthew Sparrow.
But Scunthorpe did go in front in the 68th minute when striker Billy Sharp dispossessed defender Kevin Austin inside the box and went on to fire a right-foot shot through the legs of Gueret.
Swansea were wobbling in defence, but suddenly broke forward in the 78th minute to snatch an equaliser. Williams got forward down the left and delivered a good deep cross to the far post where Fallon out-jumped the home defence to head firmly past Murphy from close range.
In the closing minutes Scunthorpe gave a debut to Italian -born sub Andrea Ferretti, signed on loan from Cardiff, who showed some neat touches but time ran out before he could make a real impact.