Andile Jali netted nine minutes in as Bafana upset the 2014 World Cup quarter-finalists, who sit 31 places above them in the FIFA rankings.
South Africa previously beat the Central Americans 2-1 in their only other meeting in 2003, with Mashaba also leading the national team at the time.
"The boys showed they can mix it with the best in the world when their backs are against the wall. I thought we really took total control of the game in the first half and we were full value of the good lead going to the break," Mashaba said.
"The defence was water-tight and the midfield played like a well-oiled machine in the first 45 minutes. And what can I say about goalkeeper Itumeleng Khune; despite suffering a recurring hamstring injury, he marshalled his defence with aplomb. This is the spirit this team must carry going forward in the World Cup qualifiers and the Africa Cup of Nations.
“I now want to go to Honduras and finish the good job we started here. It is good to develop a winning culture ahead of meetings with Angola and next year’s Africa Cup of Nations qualifiers."
Mashaba's men next visit Honduras in San Pedro Sula on Tuesday, looking to gain further momentum for the upcoming CHAN qualifiers with Angola on October 17 and 24.
Bafana will then take on the Sable Antelopes in World Cup qualifiers in November before looking to rescue their AFCON qualifying campaign against Cameroon on February 26. Mashaba's men drew at home with Gambia and lost 3-1 at Mauritania in their earlier Group M games.