The Bafana Bafana international opened the scoring after just two minutes, after being set up by Nuno Da Costa.
The hosts had a chance to level matters from the penalty spot in the 11th minute, but Thomas Mangani failed to convert from 12-yards out.
Angers were made to rue that miss as Strasbourg doubled their lead on 40 minutes, with Mothiba completed his brace on the night.
However, Angers reduced the deficit in the 58th minute thanks to a strike Pierrick Capelle, who grabbed his second goal of the season.
The comeback was complete in second-half stoppage time when Romain Thomas fired past Strasbourg goalkeeper Matz Sels to seal a point.
As a result, Strasbourg find themselves in eighth position, one point ahead of Angers, who occupy ninth.