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 has retained his form to jump to fifth on the standings.
Lowry ended a further shot back from Hillier in a tie for third with three more players, including Rory 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.