Ullman debuted after the heyday of Red Wings in the 1950s, debuting in the 1955-56 Season, but he was still on a line on with Gordie Howe and Ted Lindsay, and part of the backbone of a very good team. The Center scored at least 50 Points after his debut year for the rest of the 1950s, and he rose that to 70 in 1960-61. Ullman had his best year in a Detroit uniform in 1964-65, where he led the NHL in Goals (42), Even Strength Goals (31), and Game Winning Goals (10). For the first time in his career, Ullman was a First Team All-Star, and two years later, after his third straight 70-Point year, he was a Second Team All-Star. This was the last full year for Ullman as a Red Wing, as during the following year, he was dealt to the Toronto Maple Leafs, again arriving one year too late, as the Leafs won their last Cup in ’67.
Ullman never won a Stanley Cup but was the leading scorer in the 1963 and 1966 Playoffs, and he amassed 74 Points in 80 Playoff Games.
With the Red Wings, Ullman scored 758 Points and had 1,229 in total in the National Hockey League. Ullman entered the Hockey Hall of Fame in 1982.