The South Africans came from a goal down on Wednesday evening, took the lead and then saw it slip away as they went in search of a result to get their campaign back on track.
South Africa had a poor start to their bid for a top-10 finish as they went down to world No. 1 Australia on Monday, while Britain entered the match fresh from a 4-1 win over Argentina.
A tentative start to the opening period saw both sides feeling each other out with most of the possession heading Britain's way.
Ashley Jackson opened the scoring for Britain 13 minutes into the clash, through a penalty corner (PC), which sailed past South Africa's goalkeeper Rassie Pieterse and high into the net.
The South Africans enjoyed a better period after conceding the opener, with the majority of the possession heading their way, but the world No. 12s struggled to make the decisive pass in the final third, as opportunities went begging.
South Africa were by no means out of the contest at the break and appeared more responsive in the opening minutes of the second half as they looked to improve on giving away unforced errors in the middle of the turf.
Pieterse enjoyed another superb outing as he made several saves to keep his side in the match, as Britain became increasingly frustrated.
With 44 minutes down, South Africa spent more time in their opponents area, but clear chances were hard to come by as the Britain defence held firm.
Their sustained pressure resulted in South Africa's first penalty corner of the match with 11 minutes left on the clock.
Captain Austin Smith made no mistake as he scored South Africa's first goal of the Olympics from the penalty corner.
Jonty Robinson made it 2-1 a short while later to put South Africa in the lead for the first time in the fixture.
His celebrations were short-lived, however, as Britain equalised with three minutes to play.
A nervy end to the game concluded with a penalty corner awarded to Britain in the last minute which Pieterse saved to end the match on level terms.
South Africa next face Spain on Friday, looking for more positive results as they attempt to finish off the bottom of the table. – Sapa