The hosts were on a run of three successive league phase defeats, but set about ending that streak as early as the 11th minute, when Stanic tidily converted his third continental goal of the campaign from the penalty spot after Caio Vidal had been clumsily tripped by Manu Fernandez.
The goal almost drew an immediate response at the other end, where Ilaix Moriba had a shot saved, but the Spanish side were largely pedestrian and struggled to break down a deep, compact defence.
Claudio Giraldez’s men looked most dangerous when they released Ferran Jutgla down the right, and he floated one dangerous cross to the back post, from where Moriba headed too close to Hendrik Bonmann.
Two further attacks down the same flank provided openings for Angel Arcos and Borja Iglesias, who both missed the target. Prior to those, the Eagles should have doubled their lead, but Vidal was unable to profit from a calamitous error by Yoel Lago when he pounced on a missed kick and fired haplessly wide with only the goalkeeper to beat.
The Bulgarian outfit did not have to wait long for a second, though, making it 2-0 straight after half-time when Stanic scored again, this time whipping a beautiful strike into the bottom corner from 20 yards.
He soon completed his hat-trick with yet another penalty, as VAR intervened to give a foul for a second trip on Vidal by Fernandez, who was having a night to forget.
It had been a miserable performance to that point for Celta, but they gave the travelling fans something to cheer when substitute Pablo Duran latched onto a perfectly-weighted Bryan Zaragoza pass and slotted past the goalkeeper.
That set up a blockbuster final 20 minutes, and Moriba should have pulled another back when he was left unmarked near the penalty spot, but he was thwarted by Bonmann.
Ludogorets seemed to have stemmed the tide, and could have made it 4-1 when Vidal had a low drive saved, but they were then given an almighty scare deep into added time when Jones El-Abdellaoui converted a sensational volley that rocketed into the net.
The Bulgarians hung on, though, and move into the top 24 with a stirring win, whereas Os Celestes suffered just their second defeat since the back end of September.
Flashscore Man of the Match: Petar Stanic (Ludogorets)
