The Swedish-Spanish combination defeated Pedro Vera and Vasquez' former partner Ignacio Piotto by 6-4 3-6 6-2 to earn their place in the main draw.
It is the first time in Vasquez' career he has qualified for an Open or Master event, becoming the third Swede to do so after Amanda Girdo and Daniel Windahl.
Top-seeded qualifying couple Javi Martinez and Rafa Mendez had fewer problems in their final, defeating Adrian Ronco and Jose Maria Mouliaa in under an hour by 6-0 6-2.
Iñigo Jofre (ESP)/Luis Hernandez (ESP) v Miguel Angel Solbes (ESP)/Cristobal Garcia (ESP)
An all-Spanish duel featured next as Iñigo Jofre and Luis Hernandez faced off against Miki Solbes and Cristobal Garcia at the EuroIndoor club in Madrid.
Hernandez was the only player of the four to have qualified for a tournament already in 2023, doing so for the La Rioja Open.
That experience seemed to help Hernandez, as he and Jofre needed a single break in both sets to win the final 6-3 6-4.
The 46th-ranked couple for the tournament is through to the main draw, where their opponent is yet to be determined.
Enrique Goenaga (ESP)/Jairo Bautista (ESP) v Alvaro Cepero (ESP)/Arnau Ayats (ESP)
Finally, youngsters Enrique Goenaga and Jairo Bautista were in action against two-seed Alvaro Cepero and Arnau Ayats.
Cepero and Ayats had qualified for both Abu Dhabi and Chile already and were heavy favourites on Sunday, but were engaged in a long, tough duel by their fellow countrymen.
The match would go to the tie-break, Cepero and Ayats fighting back 3-6 after losing the opening set 6-4 to Goenaga and Bautista.
In the decider, the match got drawn out into a tie-break, where underdogs Goenaga and Bautista prevailed 7-6(6) to make the main draw.