United now have 34 points from their 28 games, and while mathematically they could still finish in 15th place, it is a highly unlikely scenario.
Both teams showed their attacking intent early on, with four chances shared before the opening goal in the 23rd minute.
Maritzburg came close to altering the score-board in the sixth minute when Ghana midfielder John Arwuah had a close-range shot saved by Nigerian goalkeeper Greg Etafia, while in the 14th minute Fadlu Davids sent a header over the bar.
Swallows' chances both fell to Sandile Ndlovu, but he headed a Mark Haskins cross over in the seventh minute before having a shot blocked three minutes later.
Good work down the right flank by Sipho Mngomezulu saw the Team of Choice going in front as Sylla Mbemba buried his header into the back of the net.
Boosted by their breakthrough, Gordon Igesund's charges continued to take the game to the visiting side and more opportunities soon followed as Mbemba had another header saved by Etafia and Mngomezulu went wide from 25-yards out.
The KZN side were rewarded for their positive play when Davids picked up on a pass from Tony Tsabedze in the 38th minute and struck a superb low long-range shot past Etafia.
Swallows needed to make an early breakthrough in the second half if they were to harbour any ambitions of a comeback and this was achieved - just six minutes after the restart Kagiso Denge struck with a rare goal, crashing an excellent 20-yarder into the roof of the net with his left foot.
Looking at the possibility of throwing away their first-half lead, the relegation-threatened United could have been forgiven for letting nerves get the better of them.
But they stuck to their guns, creating chances through Brice Aka and Tsabedze (a free kick), before Arwuah restored the two goal cushion as he headed home Mngomezulu’s cross in the 75th minute.
Cecil Oerson looked to try and pull a goal back for the Soweto side with eight minutes to go, but United keeper Michel Babale was up to the task, tipping the ball over the bar.