Flood levelled the scores with a shot from the right touchline and temporarily lifted a home side desperate to end a disastrous run.
Middlesbrough were hit with a crippling list of injuries before the kick-off. A local evening paper carried a 'fancy a game?' appeal to fans.
With so many senior players out of action manager Gordon Strachan was forced to name three teenagers on the substitute bench. They were Cameron Park (17) and 16-year-olds Luke Williams and Bruno Pilatos.
It was the youngest substitutes' bench ever named by Middlesbrough.
Boro began the season optimistic of an automatic return to the Premier League following relegation last season. Since October, however, the team have slumped alarmingly and now face a fight to even reach the play-offs.
Swansea, on the other hand, have come a long way since they suffered a 3-0 early season defeat to Middlesbrough and could have an exciting end to the season.
Middlesbrough opened on the attack and Leroy Lita had two good chances to mark his return after a three-match suspension.
Adam Johnson, returned for Middlesbrough after a hamstring injury, shot wide from 25 yards.
For Swansea Gorka Pintado, known as the Spanish Bull, was off target with a header.
Boro held the balance of play in the first half without looking a dangerous force. In fact, neither goalkeeper had a shot worthy of note to save before the break.
Lita appealed for a penalty when he was brought down but the referee was not impressed and rightly waived on play.
Swansea made an excellent start after the break. The second half was only two minutes old when Pintado put them ahead following a right-wing cross by Joe Allen.
The goal gave the 331 Swansea fans something to cheer after their long journey to the North East.
Pintado was not far off the target with a header shortly after before the home side grabbed a lifeline through Flood.
It was one of the best goals seen at the Riverside Stadium for a long time, but overall the standard of football was disappointing.