Sinclair had the breakout game she was looking for, scoring twice after being shut out in Canada's 2-1 loss to Japan on Thursday, and the team will need more games like this from its captain.
"We said winning was the only option today," Canadian head coach John Herdman said in a release. "We hopefully got what we needed. We could have had more, but that's football sometimes."
Canada (1-1-0) sits third in Group D, behind Sweden (1-0-1) and Japan (1-0-1), who played to a scoreless draw earlier Saturday. The Canadians need to finish in the top two of their group, or be one of the two best third-place teams in the tourney, to advance to the quarter-finals.
Tancredi's early strike
Tancredi scored the eventual winner in the seventh minute, redirecting a sharp cross from midfielder Diana Matheson just inside the South African six-yard box and past goalkeeper Thokozile Mndaweni.
It was Tancredi's second goal of this Olympic tournament and 20th international goal of her career.
Matheson almost doubled the Canadian lead three minutes later when she caught Mndaweni off guard, forcing her to punch away Matheson's shot, which deflected sharply off the crossbar and out of harm's way.
The South Africans didn't get the same bounces off the bar in the second half. Sinclair hammered home her own ricocheted rebound for a two-goal lead in the 58th minute, but the Canadian captain wasn't done there. Sinclair added the third goal on a breakaway in the 86th minute for her 139th international goal, that placed her level with American Abby Wambach for second place on the all-time goal scoring list. For a short time, anyway.
Wambach scored her 140th goal in a 3-0 U.S. win over Colombia on Saturday.
Canada swapped starting goalkeepers for their second preliminary match — Karina LeBlanc posted a clean sheet in place of Erin McLeod, who was in goal for Canada's tournament-opening 2-1 loss to Japan on Thursday.
LeBlanc and one of her defenders had a big scare in the 31st minute when their wires were crossed over a loose ball in the penalty area. Robyn Gayle — in for injured central defender Candace Chapman — and the keeper couldn't decide on who was to corral the ball, which was picked up by South African forward Mpumi Nyandeni.
Luckily for the Canadians, the bouncing shot deflected off of Gayle, glanced off the top of the Canadian crossbar and harmlessly behind the net.
Gayle later left the game with an apparent leg injury in the 68th minute.