Vázquez's first defense was versus Takuya Muguruma in a card organized in Osaka. The fight was declared a draw, although two of the judges scored it 116-114 and 117-112 in favor of Vázquez, while the third considered it a 115-115 tie. Subsequently, he defended against Kaokor Galaxy in Thailand, losing by split decision. The scores were 112-115 and 113-115 in favor of Galaxy and 114-113 in favor of Vázquez. Three months later, he returned to action against Raúl Pérez, but lost by unanimous decision in 10 rounds. Following this defeat, Vázquez signed a contract with Felix "Tutico" Zabala who managed to secure a regional title fight against Fernie Morales. The contest was for the International Boxing Federation's Inter-Continental bantamweight championship, in twelve rounds, Vázquez earned a points victory. This was followed by a knockout victory in preparatory fight against Patrick Kamy, which was part of a card organized in Spain. On June 19, 1990, Vázquez fought against Israel Contreras, who won by knockout, earning what was regarded as an unexpected victory. After recovering from this loss, he defeated Joe Orewa to win the International Boxing Council's super bantamweight title on September 10, 1990. Vázquez closed the year with a technical knockout victory over Atenor Solar. On April 8, 1991, he defeated Paquito Openo by knockout in seven rounds. This win earned Vázquez an opportunity for the WBA's super bantamweight championship. The fight was a rematch against Raúl Pérez and it took place on March 27, 1992. After scoring a knockdown in the second round, Vázquez defeated Pérez by technical knockout in the third, when the fight was interrupted seconds after a second knockdown. After defeating Juan Batista Bisono in a preparatory fight, Vázquez began a series of successful defenses. The first of these was a majority decision over Freddy Cruz in Italy. This was followed by victories over Thierry Jacob, Luis Enrique Mendoza, Thierry Jacob, a controversial points win against Juan Polo Perez in France, Hiroaki Yokota and Yūichi Kasai in Japan and Jae-Won Choi and Orlando Canizales in the United States. Due to his tendency of competing in title fights outside of Puerto Rico, Vázquez became known as "El Viajero", Spanish for "the traveler".