Phunya Sele Sele recovered from going a goal down, and having a man sent off with more than 30 minutes to play, to claim an emphatic victory that moves them up to 21 points and gives them a major fillip in their quest to avoid relegation.
The result also dented the Birds’ title hopes as they could have leapfrogged to second on the standings if they had won, just behind leaders SuperSport United, but instead remain fourth on 32 points, five adrift of Matsatsantsa.
Celtic made two alterations to the team that started in their defeat to Kaizer Chiefs on Saturday; Cyrille Mubiala replacing Johannes Motlhaping, and Solomon Mathe coming in for Ditheko Mototo, with Thabo Nthethe moving into the backline.
Swallows had four changes from the line-up that beat Orlando Pirates on the weekend, with Goodman Mazibuko, Vincent Kobola, Davi Rancan and Cecil Oersen coming in for Lefa Tsutsulupa, Ramahlwe Mphahlele, Edward Malinga and Morgan Shivambu.
The Birds were the first to have a pop at goal, with the in-form Sandile Ndlovu firing a shot over the crossbar as early as the fourth minute. Eight minutes later he had another crack at trying to beat Patrick Tignyemb from long range, but the keeper made a comfortable save.
On the 20-minute mark, Cecil Oersen drove an angled shot just wide of the post, and it was soon the turn of Gert Schalkwyk to test out Greg Etafia’s reaction ... an examination the Nigerian easily passed.
With 28 minutes on the clock, Schalkwyk opened up the visitors’ defence and set up Petrus Mahlatsi with a good cross, but the striker was unable to direct his header on target from 12 yards out.
Just past the half-hour mark, the dangerous Mark Mayambela gave warning of his match-winning abilities with two well-struck long-range efforts that weren’t far away from causing Etafia real trouble, while Swallows’ Sibusiso Khumalo powered an angled drive wide of goal in the 39th minute.
With the interval rapidly approaching, Celtic laid siege to the Swallows goal through Mayambela, Schalkwyk and Moses Spandeel, though only the former was able to force Etafia into any kind of save; the keeper parrying his shot away to safety.
The Birds would have been relieved to hear the half-time whistle after the hosts had built up a head of steam, and things got even better for them four minutes after the restart when Oersen opened the scoring, finding the back of the net from a free-kick after Mubiala had fouled the hard-running Radebe.
But Swallows’ lead lasted just two minutes before Mahlatsi latched onto a good pass from Mubiala in the penalty area and rippled the net from close range. Birds coach Julio Leal must have been fuming at his side’s lapse in defence so soon after establishing an advantage.
And just two minutes later Mahlatsi should have grabbed a second, screwing the ball wide of goal from six yards out after beating his marker to Nthethe’s cross.
The momentum seemed to be with Celtic, but just before the hour-mark they were dealt a major blow when defender Mario Booysen picked up his second yellow card.
Swallows almost immediately went on the offensive through Kagiso Denge and Ndlovu, while on 70 minutes substitute Shaun Haschick saw his left-footed shot from 12 yards out tipped over the crossbar.
However, Celtic defied their numerical disadvantage to take the lead for the first time with just over a quarter-of-an-hour to play. Schalkwyk latched onto a header from Spandeel and placed the ball beyond Etafia from 20 yards out to make it 2-1 in favour of the hosts.
And the on-loan Chiefs player then turned provider for substitute Tlou Segolela to score his first goal in Celtic colours in the 88th minute, quickly followed by a second from the youngster two minutes later.