While playing for the Chicago Stags, Zaslofsky was named All-NBA First Team 1946–47 at the age of 21. He held the distinction of being the youngest player named such for nearly 60 years until he was surpassed by LeBron James (2005–06). The next season, 1947-48, he led the league in scoring. At 22 years, 121 days old, he was the youngest player to lead the league in scoring until 2010, when Kevin Durant broke his mark. In 1949–50 he led the league in free throw percentage.
After the Stags broke up, Zaslofsky joined the New York Knicks. In 1956 he ended his career as 3rd leading scorer all-time (up to that point), behind George Mikan and Joe Fulks. In addition to his 1946–47 All-NBA First Team honors, Zaslofsky was named to the All-NBA First Team in 1947–48, 1948–49, and 1949–50. He also played in the 1952 NBA All-Star Game.