The Spaniard, who had struggled early in the round, duly parred the hole for an unexpected but nonetheless welcome and important victory.
Elvira told Sky Sports: “It means the world. If you had told me on Tuesday that I was going to be winning this I would never have believed you. It is a dream come true.”
Elvira finished on a 10-under par total of 274, one shot in front of New Zealander Hillier who carded a 65 and takes home $521,149 (€258,404). Fellow Kiwi Ryan Fox finished in a share of 27th after an even par 71 saw him end the tournament at two-over.
After missing the PGA Tour by two spots last year, Hillier retained his form to jump to fifth on the standings with the six-under round. Starting the day at three-under, Hillier had birdies at the second and third holes to move to five-under through the front nine. He then made his move on the back nine first with a birdie at the par five 10th followed by an eagle at the 13th, also a par five.
Another birdie at the 15th lifted Hillier a share of the lead with Rory McIlroy and Elvira but long birdie looks on the final three holes didn’t drop as he had to wait out the final round contenders.
“To be honest, at the start of the week I was chatting with Foxy, and we had a couple of nine-hole matches and he said, ‘Why can’t you be like this when you’re playing in a tournament?’,” Hillier said after this final round.
“Just pretend I was playing a little nine-hole match against the golf course, and basically taking it one shot at a time. For the most part, happy days.”
Lowry ended a further shot back from Hillier in a tie for third with three more players, including McIlroy.
McIlroy, who started the final round three shots off the lead, forced his way into contention as Elvira faltered, and briefly held a share of an increasingly crowded leaderboard.
Lowry, bidding for his first DP World Tour title since the 2022 BMW PGA Championship, looked to have made the decisive move with a 25-foot birdie on the 15th to move to the top of the leaderboard.
And when McIlroy pulled his birdie chance wide on the 17th, he set up a golden opportunity for his close friend.
But moments after Lowry had powered his second shot on the 18th into the water, Elvira birdied the 17th to seize control.
Hillier’s six-under-par final round of 65 had him hoping for at least a playoff, but Elvira, who had seen his overnight lead wiped out after successive early bogeys, held firm.