Alexis Sanchez's late penalty gave Arsenal all three points.
It came after an enthralling contest at the Emirates that had seen Mustafi and Burnley's Andre Gray each find the net.
Arsenal secured all three points despite having Granit Xhaka dismissed in the 65th minute.
Shkodran Mustafi helped Arsenal overcome Burnley
Alexis Sanchez coolly slotted home the winner
And Mustafi has paid tribute to Arsenal's fighting spirit.
"We played in their half for most of the game," he said.
"Then suddenly you are a man down and becomes difficult.
Alexis Sanchez rescued Arsenal again
Arsenal player ratings against Burnley
Sun, January 22, 2017
Express Sport rates how the Arsenal players got on in their Premier League clash with Burnley at the Emirates
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How did the Arsenal players get on during their clash with BurnleyWho impressed for Arsenal against Burnley?
"But we always are dangerous until the end because we believe in ourselves."
Arsenal are now second in the Premier League, five points behind league leaders Chelsea.