He finished at 16-under-par 272 and won his first European Tour title by three shots at Real Sociedad Hpica Espanola Club de Campo. Vibe-Hastrup won on the Challenge Tour six years ago.
Alejandro Canizares shot a 4-under 68 on Sunday to take second place at minus-13.
Overnight leader Daniel Vancsik was undone by one hole in the final round. He carded a quintuple-bogey nine at the fifth and never fully recovered. Vancsik finished with a 1-over 73 and took third place at 12-under 276.
Rory McIlroy, a former amateur star, shot a 2-under 70 and tied for fourth place with Gregory Bourdy, who had a 3-under 69 on Sunday. The pair finished at 11-under 277.
Vibe-Hastrup trailed Vancsik by two to start the final round, but cut it to one with a birdie at two. Vancsik birdied the third to move two ahead again, but then his disastrous fifth left him down the leaderboard.
'I still had to play a lot of golf from there,' said Vibe-Hastrup. 'I tried to play my own game, that was my mantra for the day.'
Vibe-Hastrup found himself two ahead now and extended his margin with a birdie at the eighth. The field got within two and Vibe-Hastrup's birdie at the 10th just kept him two ahead.
His lead moved to three with a birdie at the 12th, but Canizares would not go away. Canizares birdied the 14th after Vibe-Hastrup birdied 13 to stay three shots back.
Vibe-Hastrup tripped to a bogey at the 15th and the margin was trimmed to two. Vibe-Hastrup birdied 16, but so did Canizares, keeping the gap at two strokes.
Canizares, who won last year's Russian Open, bogeyed the 17th to fall three back. Vibe-Hastrup parred 17, then walked to the tee at the closing hole with a three-shot cushion.
He parred the last to earn his first European Tour win.
Emanuele Canonica shot a 3-under 69 for a solo sixth at minus-10.
Benn Barham (67), Marcus Fraser (72), Christopher Hanell (71), Sam Little (69), Santiago Luna (72), Jean Van de Velde (72) and Sam Walker (67) shared seventh place at minus-8.