The Amajimbos also have Algeria and Ghana in their group, and defeat in this match against the 2023 winners would have made qualification more difficult.
But after a lacklustre first half in which they were second best, coach Vela Khumalo’s side were excellent in the second period and wrestled control of the game before holding on for the win late on.
The top two teams in each pool advance to the quarter-finals and book a place at the 2026 FIFA Under-17 World Cup in Qatar later in the year.
The four teams that finish third in the groups are eliminated from the tournament but will contest play-offs to determine two more teams for the World Cup, making up Africa’s 10 entrants at the expanded 48-team tournament.
Senegal took the lead on 44 minutes after missing several excellent opportunities.
In the end, it was a simple header from a corner as Cheikh Thior found the back of the net from Sega Mbodji's delivery.
South Africa will be disappointed by their defending from the set-piece but could have had no arguments with the scoreline, having ridden their luck to that point and trailed 1-0 at the break.
But they were much better after half-time and, within 10 minutes, were 2-1 up.
They equalised when Aphelele Majola's through ball reached Mamelodi Sundowns’ Inganathi Simama, and he slid the ball into the net past goalkeeper Assane Sarr, who probably should have made the save but was unable to keep it out.
South Africa then took the lead as their strong start to the second half continued. A shot from 25 yards by Kaizer Chiefs’ Reotshepile Malete deflected off Thior and wrong-footed the goalkeeper, leaving him with no chance and the defender with a goal at both ends.
Senegal thought they had equalised as Cheikh Dieng crashed in a rocket shot from all of 35 yards that left Mamelodi Sundowns’ Lwandiso Radebe in the South Africa goal with no chance, but there was an offside in the build-up, meaning the goal was ruled out and South Africa could breathe again.
South Africa next face Algeria in their second Group D game on Sunday before a final pool match against Ghana on Wednesday.
They have been knocked out in the quarter-finals of the last two editions, but were runners-up in 2015 and finished fourth in 2005. Their only group-stage exit came in 2007.
This is their sixth appearance at the finals overall.