Simpson was drafted in the first round, second overall, by the Pittsburgh Penguins in the 1985 NHL Entry Draft. As an 18-year old rookie he scored 11 goals playing right wing (shifting from his natural centre ice position) with veterans Doug Shedden and Terry Ruskowski. then more than doubled that total in his second year with 26 goals. His third season saw him slotted on a line with superstar Mario Lemieux and Simpson began to fill the net 13 goals and 26 points in his first 21 games to start the 1987-88 season before a blockbuster trade would take him off the wing of one of hockey's superstars and land on the wing with another. On November 24th, 1987, Simpson, along with Dave Hannan, Chris Joseph and Moe Mantha were shipped to Edmonton in exchange for Paul Coffey, Wayne Van Dorp and Dave Hunter.