Federico Macheda scored the winner midway through the first half for the Red Devils, who came closest to increasing their lead just before time when another Italian, substitute Davide Petrucci, rattled the crossbar.
It was a closer match than anticipated, with many South Africans believing mid-table Premiership side AmaZulu would be swept aside by the former European champions even though they lacked many first choices like Wayne Rooney.
Political icon Nelson Mandela, the first democratically elected president of South Africa, was remembered before the kick-off with the teams wishing him a happy 94th birthday in song.
"My players tired during the second half which was quite even," said United manager Sir Alex Ferguson. "I'm happy with the result and it was nice to give Nelson Mandela a birthday present of a United victory.
"I gave a few young players a chance tonight and we have high hopes for two or three of them. Jesse Lingard has got a lot of potential and Scott Wootton impressed in the heart of defence."
United left new signing Shinji Kagawa from Japan on the bench as they started with a mix of experienced stars like captain Rio Ferdinand and youngsters Robbie Brady, Frederic Veseli, Wootton and Lingard.
The Red Devils were quick into their stride on a clear mid-winter evening in the Indian Ocean city and could have taken the lead inside two minutes had Javier Hernandez been sharper.
Goalkeeper Tapuwa Kapini failed to grasp a close-range Macheda shot and the ball fell invitingly for the Mexican in front of goal, but he failed to connect and the South Africans hastily cleared.
United were dominant in the early stages against nervous opponents and the 2012 English Premier League runners-up to Manchester City would not have been flattered by a three-goal lead after 10 minutes.
Machedo broke the deadlock on 20 minutes by finishing off good work from Paul Scholes and Dimitar Berbatov with a close-range shot that touched the hand of the AmaZulu goalkeeper and the foot of a defender before crossing the line.
The goal triggered greater urgency from AmaZulu, a South African Premiership side coached by Swede Roger Palmgren, and Ayanda Dlamini twice threatened the visiting defence.
Berbatov was unlucky not to score a second goal for United before half-time as his sweetly struck volley off a corner was brilliantly tipped over the bar by Zimbabwean Kapini.
A frenetic start to the second half saw both teams come close to scoring and AmaZulu posed more of a threat as it progressed, although they were continually let down by wild shooting.
Kagawa, a June signing from German champions Borussia Dortmund, finally came on one minute from time after a prolonged wait on the touchline before the ball went out of play.
United play Ajax Cape Town Saturday before flying to China for a midweek clash against Shanghai Shenhua, the club that recently signed Chelsea Champions League hero Didier Drogba.
The Old Trafford club will also face Valerenga in Norway, Barcelona in Sweden and Hanover in Germany during a 22,000-mile (35,400-kilometre) pre-season tour before opening their Premier League campaign against Everton.