Bradley Ritson had handed Usuthu the lead early in the second half before Shivambu double strike secured the points for the Dube Birds.
The hosts threatened in the very first minute of the game when Ritson tried his luck from 20 yards out, but his effort flew straight into the arms of Swallows keeper Greg Etafia.
Swallows slightly dominated in terms of possession from that point on, with Cecil Oerson, Mark van Heerden and Mark Haskins prominent in most of their attacking play.
However, despite both teams adopting a more attacking approach, neither could breach the other’s defence, with the match still goalless at half-time.
Usuthu needed just seven minutes after the restart to open their account when Ritson fired home a low shot from inside the area following a good build up by the hosts.
The goal seemed to just the tonic Swallows needed as they stepped up a gear and although they initially struggled to break the solid AmaZulu defence, they were eventually rewarded in the 70th minute when Shivambu struck with a fierce shot from inside the area.
The midfielder needed just eight minutes to double his and Swallows’ tally when he ran onto a pass by skipper Lefa Tsutsulupa, to slot home from the close range and hand the Dube Birds a deserved victory.
The Birds are eighth on the league table with 15 points, three more than the 12th placed Usuthu who have now lost six games.