Rahm joins the likes of Spanish greats Seve Ballesteros, Sergio Garcia, Alvaro Quiros and Miguel Angel Jimenez as victor of the Spanish Open.
He becomes the sixth Spaniard to win the Spanish Open since it became part of the European Tour in 1972, joining some illustrious company including Seve Ballesteros, Sergio Garcia and Miguel Angel Jimenez.
Dunne fired a third round 68 to stand at 17 under par for the tournament being played at the Centro Nacional de Golf.
Dunne got off to a nervous start quickly finding himself two behind Rahm who birdied the opening two holes while the diminutive Irishman was three behind when he bogeyed the fourth.
"When I made the decision to come straight from Augusta it wouldn't be to just show up and walk around, I wanted to win this tournament", Rahm said.
"I would love to be a champion in my country".
Dunne is 17 under, one clear of Elvira and two ahead of Rahm and Swede Henric Sturehed, in joint-third, while Australian Brett Rumford is next at 14 under. Triumph the previous one join and also I'd to win that collection of winners that are Spanish and to around my newbie and pro livelihood within such a way, it'so tricky to explain how good it feels and it is. There, he escaped with a par after nearly sending his tee shot into the water, the ball just holding up in the rough.
Rahm and Elvira were both tied at 19-under on the 15th and a playoff beckoned, but Elvira hit the water with his first shot on the penultimate hole, leading to a double bogey. George Coetzee was a shot further back in fourth after a 63.
"It's been incredible", Rahm noted. You can tell how excited everybody is, I felt that tension, I felt that stress, I felt everything magnified.
We had backed Ireland's Paul Dunne for his second European Tour victory at a handsome 22/1, following the advice of our betting guru Nick Fleming.
The 24-year-old added: "I hope there is a Spanish champion".