Rahm went in to the final round two strokes off the pace, but mixed six birdies with a sole blemish on Sunday to join the likes of Seve Ballesteros and Sergio Garcia as winners of their home event.
"I knew that if I played my game I could make birdies early on, and I started with that great drive on one and that great second shot and started with four flawless shots".
"It's truly been the hardest Sunday I've ever had in any tournament that I've won because the crowd wanted it so much and I wanted it so much", he said after signing for a final round 67.
"I've been blessed to be national champion from 16 to all ages in Spain", he added.
It gave him a two-shot victory over Ireland's Paul Dunne.
"I hit a lot of chips that I thought were better than they were but kept misjudging bounces". So while I feel good for the next few weeks, I am disappointed not to win.
The tournament was eventually decided on the short 17th as Rahm escaped with a par after nearly sending his tee shot into the water, the ball just holding up in the rough.
Two ahead playing the par-five 18th, Rahm reduced it to a drive, a mid-iron and two putts on greens that were far from ideal. Everyone seemed to want me to win.
Rahm soon found himself in the solo lead as Elvira and Dunne both missed the green and failed to get up and down on the fourth but Elvira snatched top spot with an eagle on the next, holing a downhill left-to-righter from 35 feet. They were pushing me so hard and I felt that. I tried to isolate myself, but I could feel it.
"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.
Further back, George Coetzee enjoyed an impressive final round as he ended the day on nine under, seeing him claim fourth place ahead of four others tied for fifth.
Rahm then birdied to one clear on 18-under but dropped a shot on nine with Dunne parring four holes in succession from the sixth with the duo heading to the closing nine locked at 17-under.
"I'm just happy to play the way I did and to get it done", Rahm told Sky Sports after his third European Tour victory.