Percy Tau fired a spot-kick wide in the opening half in Korhogo and it proved a costly miss as the clinical Eagles were never in danger after netting twice.
Victory took Mali to the top of the group on goal difference from Namibia, who shocked Tunisia 1-0 in the first match of a double-header.
Mali are a bogey team for South Africa, having twice eliminated them in the quarter-finals in previous Cup of Nations meetings.
The Malians came closest to winning the African showpiece in their 1972 debut as they reached the final before losing 3-2 to Congo Brazzaville in Yaounde.
South Africa did better in their first appearance 24 years later, defeating Tunisia 2-0 in the final in Johannesburg, but have not lifted the trophy again in nine subsequent appearances.
While Mali did not have a single home-based player in the starting line-up, South Africa chose nine, including seven from domestic giants Mamelodi Sundowns.
The mainly Mali-supporting crowd in the 20,000-capacity stadium built in the northern city for the Cup of Nations saw a lively end-to-end start to a much-anticipated showdown.
South Africa squandered a chance to take the lead on 19 minutes when Tau, who plays for Egyptian and African giants Al Ahly, blazed a penalty over the crossbar to his huge embarrassment.
It was awarded after the referee went to the VAR touchline monitor and saw Sikou Niakate elbow Evidence Makgopa after Aubrey Modiba crossed into the area.
South Africa were almost made to pay for the missed spot-kick in first-half added time when Sinayoko was foiled by goalkeeper Ronwen Williams.
A couple of Bafana Bafana defenders failed to clear the ball, allowing Sinayoko to break clear but Williams dashed off his line to divert the ball away from danger.
Mali should have gone in front soon after half-time but Amadou Haidara fired wildly off-target from close range with only the goalkeeper to beat.
However, the Eagles did take the lead on 60 minutes thanks to the alertness of captain Traore after a free-kick.
The Sekou Koita set-piece beat Williams only to rebound off the underside of the crossbar and Traore reacted quickest to push the ball into the net.
Just six minutes later Mali were two goals ahead as Sinayoko demonstrated his physical strength by brushing aside Siyanda Xulu and slotting the ball into the net from close range.
In the second round of Group E matches, Mali face Tunisia on Saturday and Namibia meet South Africa on Sunday with both matches in Korhogo.
AFP