The centre-back, who was named Man of the Match, struck in the 34th and 67th minute of the last-16 tie, with striker Knowledge Musona adding a third goal late on at Peter Mokaba Stadium.
Mashamaite previously bagged a brace when playing for Bidvest Wits in a 4-2 defeat of Mamelodi Sundowns in 2009.
He told Chiefs' official website: "It is not the first time I scored a brace but each time you score as a defender it becomes special. This is a modern game where everyone in the team is a potential goal scorer. I don't only think about defending, I visualise scoring goals also.
"I am glad to contribute to the success of the Kaizer Chiefs family. Soccer is a project and I am happy to see my progress. There are still areas that need polishing but so far so good. I hope to improve and look forward to happier moments going forward.
"I am happy to hear people saying I have a penchant for goals when I play in my home town of Polokwane. I appreciate that but I would like to be seen scoring goals anywhere we play.
"I am humbled and would like to thank my teammates for the team work. I will be happy when we start to hit the right zone and once we get to the tempo that saw us win the league and cup double last season," concluded the former Clever Boys captain.