Bennett Chenene's goal gave Swallows the lead until was cancelled out by Sibusiso Vilakazi's strike nine minutes from the end.
With three minutes gone in the match, Swallows were awarded a free-kick from just outside the box. Their skipper Lefa Tsutsulupa stepped up and his shot went through the wall, but Wits keeper Jackson Mabokgwane swiftly moved to handle the ball after the set piece was taken quickly.
Tsutsulupa and Mabokgwane again resumed their rivalry from a dead ball situation in the 20th minute. The midfielder's strike from just outside the box and dipped into the target but Mabokgwane was on hand to flick the ball over the bar.
In the 27th minute Wits had their first real sight at goal when Sibusiso Vilakazi's shot went wide of goal after brilliant link up play with striker Ryan Chapman. Wits were applying pressure on Bird's defence.
In the 50th minute of the match the Dube Birds fluffed a crucial opportunity to take the lead. Veteran attacker Siyabonga Nomvete's trickery down the left wing saw him send a decent cross into the box which was met by his pint-sized teammate Dikgang Mabalane, but the winger headed wide from six yards with the Wits defence at his mercy.
In the 64th minute of the match the home side took the lead through Chenene. Joseph Makhanya made an intelligent run down the right flank into the box and dragged the ball back for his former Orlando Pirates colleague to tap home from close range.
Swallows could have doubled their lead in the 79th minute when Chenene's shot was blocked from close range by the Wits keeper after a nice through back-heeled ball by Tsutsulupa. But two minutes later at the end the Dube Birds were made to pay.
Second half substitute Calvin Kadi found Vilakazi with an inch perfect pass and the midfielder poked his effort with power to make it 1-1 as he beat Swallows keeper Greg Etafia at his near post.