In the 1987-1988 season, Simpson joined the Oilers, a team that was in the midst of establishing itself as one of the most dominant franchises in NHL history. His arrival in Edmonton marked the beginning of a highly successful period for both him and the team.
Simpson played alongside hockey legends such as Wayne Gretzky, Mark Messier, Jari Kurri, and others during his time with the Oilers. He contributed significantly to the team's offensive prowess, adding scoring depth to an already formidable lineup. The pinnacle of his playing career with the Oilers came in the 1987-1988 season when the team won the Stanley Cup. Simpson's offensive contributions during the playoffs were crucial to the Oilers' success.