Grant Leadbitter fired Boro into a shock lead before Anthony Martial and Paul Pogba struck twice in 90 seconds to complete a thrilling turnaround.
The closing stages saw attacking midfielder Mkhitaryan deployed in defence and Mourinho explained why in his post-match press conference.
“I put Mkhitaryan at left-back when we scored the second goal because at 1-0 it was Negredo and Traore against Bailly and Rojo – two against two,” he said.
“Valencia was the winger, we had no left-back and we went for everything.
“Then when we scored the second goal, obviously, we started to close.
“I thought Micki was really fresh and could do a better job at left-back than other players and I wanted to keep Herrera and Pogba in the middle, and we managed to keep the 2-1.”