Monti was a rugged and ruthless player, but had the technical skills to go with his strong tackling. He played as an attacking centre half in the old-fashioned Metodo system: a position roughly equivalent to the defensive central midfield position of today. As such he would mark the opposing centre forward when his team were defending, but would be the main midfield playmaker when his team were on the attack. He was nicknamed doble ancho (double wide) due to his coverage of the pitch.
Monti started his career in 1921 with Huracán, where he won the first of his many championships. The following year he signed with Boca Juniors but left without playing a game. He joined San Lorenzo where he won a further three Argentine championships. All of Monti's honours in Argentina were recorded during the Amateur Era.
In 1931 Monti was signed by the Italian club Juventus, as he had Italian citizenship. As he was overweight and out of condition, he had a month's solitary training. Monti was back to top form helping Juventus to four consecutive Serie A titles (1932 to 1935). Monti went on to play 225 matches and score 19 goals in Italy.
The Battle of Highbury is a match that took place between Italy and England on November 14, 1934 at Highbury, the home ground of Arsenal. Monti was playing centre half for Italy, but as early as the second minute he broke a bone in his foot after a clash with England centre forward Ted Drake. Down to 10 men, in the days before substitutes, Italy succumbed 2–3. Monti was only to play twice more for Italy.
In total Monti won 16 caps (5 goals) for Argentina between 1924 and 1931, and 18 caps (1 goal) for Italy between 1932 and 1936.