An 89th-minute goal from substitute Gary Liggett earned Dungannon a point against Ballinamallard at Ferney Park.
Emmett Friars and James McKenna went close for the Mallards in the first half, before McKenna opened the scoring 10 minutes after the interval.
McKenna twice feigned to shoot and then completed an expert finish into the bottom corner past Andy Coleman.
The Swifts were reduced to 10 men two minutes into added time when Andrew Burns was sent-off for a second yellow.
The hosts carved out several chances in the opening period but Friars headed just wide from Jason McCartney's free-kick.
Coleman tipped over another Friars header, while McKenna had an effort cleared off the line after a McCartney corner.
Liggett secured a draw a minute from time with a looping header over Alvin Rouse.
Whitey Anderson's side retain a one-point lead over their ninth-placed visitors in the table.
What they said
Ballinamallard manager Whitey Anderson: "I feel sorry for my players as they gave it everything they had and were only two minutes away from getting a deserved three points. I can't fault our commitment at all."
Dungannon manager Rodney McAree: "We have improved in recent weeks and if we had done better in the final third we could have got more from this game.
"We didn't create enough and our delivery when we got into wide areas was poor. We need to improve on that."