The result left Serbia second in the section on eight points from four games, two behind leaders Ireland who were 1-0 winners in Austria. Wales are third on six points while fourth-placed Austria have four.
Bale fired the Welsh ahead with his 26th international goal when he unleashed a sizzling low shot in the 30th minute to close in on their all-time leading scorer Ian Rush (28).
Bale missed a golden opportunity to double the home side's lead moments before Serbia struck at the other end, when Mitrovic got away from his marker to head home Antonio Rukavina's cross from the right.