A native of Havana, Luque debuted with the Boston Braves in . In , he was traded to the Cincinnati Reds, with whom he would play the next 12 seasons. In the notorious World Series, he appeared in two games as a relief pitcher. Luque also played for the Brooklyn Robins/Dodgers from to and with the New York Giants from to . He was with the Giants in the 1933 World Series, and, pitching in relief, won the 5th and final game over the Washington Senators. He ended his career with a record of 194-179 and a 3.24 ERA.
Luque became a starting pitcher in . Although leading the National League in losses in , he had his best year in , leading the league with 27 wins and an ERA of 1.93. Luque also led the NL in ERA with a 2.63 in .
Luque's primary pitch was a curveball. Therefore, he was very analytical in his pitching. His attention to detail made him an adept teacher in his later years, and Luque served as pitching coach of the Giants from 1936-38 and 1942-45.
As a blue-eyed, fair-skinned, white Cuban, he was one of several white Cubans to make it in Major League Baseball at a time when non-whites were excluded. Between and alone, seventeen Cuban-born Caucasian players played in the Major Leagues.
Luque was inducted into the Cincinnati Reds Hall of Fame in 1967.
He had a hot temper, and usually kept it under control. One day, however, when he was with the Brooklyn Dodgers, a heckler in the stands tested Luque's temper by hollering at him "Lucky Luque! Lucky Luque!" over and over until he almost drove the pitcher crazy. Luque went over to the dugout and told manager Wilbert Robinson, "I tell you, Robbie, if this guy don't shut up, I'm gonna shut him up." "Aw, come on, Dolf," said the manager. "He paid his way in--let him boo." Just then the heckler spotted the rotund Robinson and yelled, "Hey, fat belly!" Robinson said, "OK, Dolf--go ahead and clobber the jerk." Robinson never looked up as Luque did just that. (Source: Baseball's Greatest Managers, 1960)
He is buried at Colon Cemetery, Havana.