Swallows dominated the encounter but needed an equaliser from Luvhengo Mungomeni to cancel out substitute Thokozani Sekotlong's 69th minute opener.
The result sees the Dube Birds inch a point ahead of Matsatsantsa and AmaZulu, who face each other at 20h15.
Platinum Stars, who visit champions Kaizer Chiefs at the same time, are two points off the pace, while Mamelodi Sundowns and Bidvest Wits are also eyeing top spot as they battle one another this evening.
In a goalless opening period, The Team of Choice had the first chance, as new signing Yakubu Mohammed had a low shot gathered by Swallows goalkeeper Greg Etafia.
At the other end, evergreen striker Siyabonga Nomvethe headed just wide following a left-wing cross from Levi Mokgothu in the 21st minute.
A minute later United's Ashley Hartog came off the field with a hamstring injury, with veteran midfielder Dillon Sheppard taking his place.
The Dube Birds nearly scored the opener just shy of 30 minutes, but goalkeeper Shu-Aib Walters pulled off a magnificent save to deny Nomvethe's volley from close range following a ball over the top from Man of the Match Lerato Chabangu.
Walters came to his team's rescue again just before the break, dropping down smartly to foil Edward Manqele's powerful strike following a through-ball from Lefa Tsutsulupa.
United suffered another injury setback in the 48th minute, as Mohammed limped off the field with a knock, prompting the introduction of Sekotlong.
Swallows were less dominant after the break, although Nomvethe threatened with a venomous drive from range just past the hour-mark.
Sekotlong then broke the deadlock against the run of play when he steered in a cross from fellow injury-enforced replacement Sheppard.
The lead, however, was short-lived as Mungomeni nodded in a cross from the right by substitute Dikgang Mabalane, on for Tsutsulupa, in the 76th minute.
Neither side could snatch a winner in the tense closing stages.