The duo had shared the lead midway through the second leg of the rally, and they each won two of the remaining four stages on Saturday.
The lead changed hands between the reigning series champion and his Italian opponent on several occasions, but top place on the podium was settled on the final, all-gravel stage as Basso finished with a total time just 2.8 seconds quicker than Mikkelsen.
Basso's victory came despite him winning one stage fewer than Mikkelsen, who had claimed all three stages contested on Monte Benedetto.
However, second place was enough Mikkelsen to extend his championship lead over Jan Kopecky to 31 points.
Another Italian, Umberto Scandola, was a distant third, 1:41.6 off the lead.
"I'm very happy," said Basso, whose victory was his first in the IRC since 2009. "It was a fantastic race and battle with Andreas, who is a very good driver. My team has done a great job and the car and tyres have been perfect."