Dunne attended Blackrock College, a secondary school for boys where he was trained by personal trainer Matthew Looby. Dunne played college golf at University of Alabama at Birmingham, which Graeme McDowell also attended. As a senior, Dunne finished fifth in the individual competition at the 2015 National Collegiate Athletic Association Division I Men"s Golf Championship.
He first came to prominence at the 2015 Open Championship where, playing as an amateur, he was tied for the lead after three rounds. As a junior, he was named the 2014 Conference United States of America Golfer of the Year. As a senior in college he was the Blazers" top golfer with a scoring average of 71.9.
Dunne qualified for the 2014 Open Championship through final qualifying at Woburn.
He scored 75 and 73 and missed the cut by two shots. He also played in the 2014 Palmer Cup.
2015 Open Championship Scoring 69 in each of the first two rounds at Street Andrews, he made the cut and was the leading amateur at that stage. In the third round, he scored 66 to become joint leader at 12-under-par.
He was the first amateur since 1927 to lead the Open Championship after 54 holes, and he also set a tournament record for lowest 54-hole score by an amateur.
On the final day he was in the last pairing with Louis Oosthuizen. He shot a 78 in the final round to drop to a tie for 30th place. Dunne turned professional later in 2015.
His first event as a pro was the Alfred Dunhill Links Championship.
2009 Irish Boys Close DNP = Did not play CUT = missed the half-way cut "T" = tied Amateur Jacques Léglise Trophy (representing Great Britain & Ireland): 2009 (captain, winners) Palmer Cup (representing Great Britain & Ireland): 2014 (winners) Eisenhower Trophy (representing Ireland): 2014 Walker Cup (representing Great Britain & Ireland): 2015 (winners).
