In 1982–83, Gregg emerged as a regular on the Oilers' blueline, appearing in all 80 games and registering 6 goals and 28 points. Receiving as much notoriety from the fact that he had a medical degree as he did for his solid play on the blueline, he helped the Oilers reach the Stanley Cup finals in 1983. In 1983–84, he would have his finest NHL season, as he recorded career highs of 12 goals and 40 points, and then contributed 10 points in 19 playoff games to help Edmonton win their first Stanley Cup. Following the season, he was selected to represent Canada at the 1984 Canada Cup tournament.