Barrios was runner-up in the 1963
Open de España but he was at his best during the late 1960s and early 1970s. He was runner-up in the 1970
Italian BP Open and the 1970
German Open and won the 1971
Madrid Open and the 1972
Algarve Open. Representing Spain, he partnered with
Ángel Gallardo and won the 1972
Marlboro Nations' Cup, beating the Welsh pair of
Brian Huggett and
David Vaughan in the final. He also won the 1973 Lancia D'Oro invitation tournament at Biella Golf Club near
Magnano, Italy. Barrios played on the
European Tour in the 1970s. He never won a European Tour event but one the European circuit events he won, the 1971
Madrid Open, would be incorporated into the European Tour while the
Lancia d'Oro, which he won in 1973, was part of the European Tour the previous season. His best finishes on the European Tour was second place which he recorded three times: at the 1972
Spanish Open, 1972
Italian Open, and 1974
Madrid Open. He twice lost in a playoff, at the third playoff hole against
Antonio Garrido in the 1972 Spanish Open and at the first playoff hole at the 1974 Madrid Open. ==Professional wins (3)==