Scotland ran out 2-0 winners thanks to goals from Christophe Berra and Leigh Griffiths to keep their hopes of qualifying for next summer's World Cup alive.
However, the match was marred by an incident in the second half with Malta's Borg allegedly spitting on Brown.
Brown told reporters after the game: "He [Borg] did spit on me. He put his hand up to apologise but I managed to keep my head and the main thing was getting the three points.
"It was about the team, not about one guy, bookings or anything like that.
"We played really well, at our tempo. We were patient with the ball and created chances from that."