Ousmane Dembele, Andre Gomes and Suarez all scored for Barca, before Sibusiso Vilakazi replied for the hosts. He came on for the last 15 minutes, enough time for him to launch a stinging, long-range shot that goalkeeper Kennedy Mweene struggled to stop.
Up next for Barcelona is a home tie against Real Sociedad in their final league game of the season.
Barcelona coach Ernesto Valverde has picked arguably his strongest squad for this assignment, including Messi, Andrés Iniesta, Luis Suarez, Ivan Rakitic, German keeper Marc-André ter Stegen, Gerard Pique and former Liverpool midfielder Phillipe Coutinho.
According to Mundo Deportivo, Barca are on a tight schedule: they arrived in Johannesburg this morning, play Sundowns this evening, then fly back to Spain on tonight - so it really is a lightning visit.
Mining magnate Patrice Motsepe, owns the Sundowns and is the fifth-wealthiest South African billionaire, will pay Barcelona £2.6million for making the one-day trip. Runway workers at South Africa's biggest airport temporarily abandoned their jobs to gather near the plane and cheer the team's arrival.