Second seed Auger-Aliassime let two championship points slip in the second set tie-break before winning 6-2, 6-7(7), 7-6(2) for his second title of 2025 after Adelaide.
"For sure, the craziest final I have played, whether I won or lost," said the 23rd-ranked Auger-Aliassime after the two-and-a-half-hour battle against a qualifier who was playing his first tour-level final.
"It was a crazy match. I couldn't have got a better start. I was feeling good, but credit to Aleks, he raised his level.
"I think it was a very high level on both ends, serving well. This match deserved to go three sets with the way he was playing in the second."
The Canadian reeled off five consecutive games from 1-2 in the first set to take control, before both players dug deep in a second set that did not feature a break point.
Auger-Aliassime twice held championship point on return at 6/5 and behind his own serve at 7/6, but 102nd-ranked Kovacevic earned three straight points to level the match.
In the third set, Kovacevic had one break point before his opponent held serve for 6-5 and swept to the title in the tiebreak.