Gillick, who served 27 years as a general manager for the World Series champion Toronto Blue Jays and Philadelphia Phillies as well as for other teams, was inducted first, becoming the 32nd executive to be elected to the Hall.
Alomar, meanwhile, played second base on two of Gillick's championship squads -- the 1992 and 1993 Blue Jays.
Inducted in just his second year on the ballot, the Puerto Rico native is a 12-time all-star and won 10 Gold Gloves at his position.
Blyleven followed, accepting his HOF plaque after waiting 13 years for the honors. The right-handed pitcher known for his curveball racked up 287 wins in his long career, spent mainly with the Minnesota Twins, Pittsburgh Pirates and Texas Rangers.
The Netherlands native won World Series championships in 1979 with the Pirates and 1987 with the Twins.