An own goal from Lwamba gave Galaxy a 1-0 half-time lead, but the KwaZulu-Natal side turned it around in the second period as Mfanafuthi Mkhize and Lwamba netted, with City becoming the first club from their province to lift the trophy.
City claimed the Nedbank Cup for the first time in their history, having lost the 2018 decider to Free State Stars when the club still campaigned as Maritzburg United.
It was a reward for their interim coach Pitso Dladla, who won the first major trophy of his career.
Galaxy, who were 2019 winners while still in the second tier, could not repeat that feat in their second final appearance.
Remarkably, the last five Nedbank Cup finals have all ended with 2-1 scorelines, while the four before that all ended 1-0. Before this current run of 2-1 scores, there had never been a final that finished with that scoreline.
Galaxy’s Victor Letsoalo blazed over at the back post after being set up by Mpho Mvelase in a huge chance for The Rockets midway through the opening period.
Galaxy took the lead in the 43rd minute as Letsoalo's rocket header was only parried by Durban City goalkeeper Darren Keet, and it looked as though City's Lwamba put the ball into his own net from close range under pressure from Seluleko Mahlambi.
It is not the first time an own goal has been scored in the Nedbank Cup final. Orlando Pirates’ Rooi Mahamutsa put the ball into his own net against Black Leopards in 2011, while Clayton Daniels did likewise for SuperSport United, also against Pirates, in 2016 at the Peter Mokaba Stadium. But on both occasions, their teams still came out on top.
Durban City enjoyed the majority of possession in the first half and led on Expected Goals, 0.41 to 0.23, but Galaxy had the only shot on target in what was a cagey opening period.
There was heartbreak for teenage centre-back Mlondi Mncwango when he was forced off with a leg injury early in the second period in what was just his second appearance as a professional. He was replaced by the more experienced MacBeth Mahlangu.
City were level just before the hour-mark when Luphumlo Sifumba’s low cross eluded everybody in the box and reached Mkhize at the back post, and he fired in the equaliser with his side’s first shot on target.
It was just the second goal Galaxy had conceded in this year’s Nedbank Cup, and the second City had scored through one of their own players.
Lwamba made up for his earlier own goal when he netted at the right end with a superb strike after he was fed on the edge of the box by Sifumba, with his finish with the outside of the boot looping over Ira Tape in the Galaxy goal.
This was just the fifth Nedbank Cup final since 2008 that did not feature one of Kaizer Chiefs, Orlando Pirates or Mamelodi Sundowns. The others were in 2009, as Moroka Swallows beat University of Pretoria; 2010, when BidVest Wits defeated AmaZulu; 2018, as Free State Stars edged Maritzburg United; and 2021, when Tshakhuma Tsha Madzivhandila, now Marumo Gallants, defeated Chippa United.