Throughout the majority of the final round at Muirfield Village Golf Club, McCarthy held a two-shot advantage on the chasing pack courtesy of his outstanding putting under pressure.
That continued during the final stages, but Hovland got himself back to within one shot with a long-range birdie on the 17th, the only such score on that hole all day.
A poor tee shot on the 18th put McCarthy on the defensive as he bid to win his first PGA Tour title and after missing a 23-foot putt for victory, he had to make a five-footer coming back to force extra holes.
However, another poor opening shot on the last, this time on the opposite side, left McCarthy needing to make a 14-footer for putt, but once that agonisingly missed to the left, Hovland converted from seven feet for the biggest triumph of his career.
The round of the day came from world number one Scottie Scheffler, who held the clubhouse until the closing stages courtesy of a five-under-par round of 67 earned him third place.
A miraculous chip in at the fourth gave the Northern Irishman the momentum that he required, but he made seven bogeys between the fifth and 17th holes to have to settle for a share of seventh position.