Rune came into the game lacking match practise as he hadn't played since he crashed out against Mariano Navone in the round of the last 16 in the ATP tournament in Buenos Aires on 13 Feburary where he suffered from illness.
Its not the first time that the Spaniard, who is number 50 in the world rankings, has turned into a tough challenge for Rune.
In 2023 the Spaniard beat Holger Rune in the first round of the US Open and Rune also struggled to control Carballes Baena's strong baseline game on the hard court surface in Mexico.
In his own serve, Rune missed two set points to close the first set and eliminate the tension when he was ahead 5-4 and 40-15 and instead lost the game.
However, Rune regained his composure and showed his mental strength in the tiebreaker, which he won 7-4.
The Dane's dominance became more evident in the second set after an exciting opening game, where the Spaniard had two break points which he failed to convert.
Rune then took a 3-0 lead before the two players took turns to hold their own serve serve as the 21-year old Dane kept his cool to prevent the drama from the first set.
Thanks to the win over the ten-year-older Spaniard, Rune now levellled the score in their individual H2H statistics.
In the second round, Holger Rune will face American Brandon Nakashima. The two players have met three times, and the Dane has never won against thte American.
Should Rune maintain his seeding in the tournament, he will face the top-seeded German, Alexander Zverev, in the semi-final
The tournament in Acapulco is the last warm-up tournament before the all important ATP 1000 tournaments in Indian Wells and Miami in March.