Hibs skipper Pat Stanton beat Evan Williams to open the scoring on the hour mark and six minutes later he crossed for Jimmy O'Rourke to head in the second goal.
Kenny Dalglish pulled one back for Jock Stein's men but the Easter Road club held on to claim their first major trophy since the 1951/52 league title.
The attendance at Hampden Park for the 1972/73 League Cup final was 71,696.
Celtic went on to retain the First Division title while Hibs finished the season in third place.
Hibernian
Jim Herriot
John Brownlie
Erich Schaedler
Pat Stanton
Jim Black
John Blackley
Alex Edwards
Jimmy O'Rourke
Alan Gordon
Alex Cropley
Arthur Duncan
Celtic
Evan Williams
Danny McGrain
Jim Brogan
Pat McCluskey
Billy McNeill
David Hay
Jimmy Johnstone
George Connelly
Kenny Dalglish
Harry Hood
Lou Macari
