The 20-year-old produced a strong comeback to overcome Montes 3-6, 6-2, 6-3 in a final lasting one hour and 57 minutes.
Balshaw dropped the opening set but responded impressively, winning the second before taking control of the deciding set to secure the biggest title of his young career.
First Challenger title
The triumph represents Balshaw's first ATP Challenger title and marks an important breakthrough in his professional career.
His victory also made him the eighth different champion in the eight editions of the Rafa Nadal Open.
The previous winners include Bernard Tomic, Emil Ruusuvuori, Lukas Lacko, Luca Nardi, Hamad Medjedovic, Duje Ajdukovic and Dani Rincón.
Balshaw's impressive week
Balshaw's run in Manacor included several notable victories as he battled through the draw to reach the final.
In the semi-finals, he defeated Mark Lajal 7-6(7), 7-5, before completing his memorable campaign against Montes in the championship match.
The Frenchman also defeated experienced French player Alexandre Müller during his run at the Challenger event.
A major career milestone
The title is a significant step forward for Balshaw, who is now beginning to make his mark on the ATP Challenger Tour.
Winning at the Rafa Nadal Academy adds further significance to the achievement, with the tournament providing a platform for emerging players to establish themselves at Challenger level.
Balshaw will now look to build on his breakthrough title as he continues his progression towards the upper levels of men's professional tennis.