During his professional playing career, he scored at least 50 points in a game 15 times.[4] His single-game career scoring high was 70 points scored, achieved during an Italian League game, between Venezia and Virtus Bologna, on 25 January 1987. He was nicknamed "The Sky Jumper".[5]
In the 1980–81 season, he went abroad for the first time in his career. During that season, he played with Reyer Venezia, of the Italian Lega Basket Serie A league. After just one season with Venezia, he returned to his former club, Partizan, for one season. In the following seasons, he played for numerous European teams, including Real Madrid, of the Spanish Primera División, during the 1982–83 season, in which he only played with the club in FIBA European Champions Cup (now called EuroLeague) games. He also played with Reyer Venezia, and Glaxo Verona of the Italian League. He finished his professional career after the 1990–91 season, in which he played with Partizan's arch-rivals, Crvena zvezda.
As a Partizan Belgrade player, he scored 8,278 points, in 305 games played, for a scoring average of 27.1 points per game. While playing in Italy, he scored 7,993 points in 241 games played, for a scoring average of 33.2 points per game. He led the Italian League in scoring average, in the 1987–88 season, with an average of 37.7 points per game.
Dalipagić finished high school at the Technical School in Mostar, and graduated from the Teachers College in Belgrade. He is married to Sonja Požeg, former Yugoslav tennis player. They have two children, Sanja and Davorin.
