Richardson curled home a wonderful winner from 20 yards with 19 minutes left to make it a winning start for a Leeds team comprising seven debutants.
Derby felt they were unlucky when Michael Johnson's header was ruled out for a foul late in the first half.
And Leeds were grateful for Neil Sullivan's injury time save from Junior after Ian Taylor hit the woodwork.
Derby manager George Burley:
"I thought we were unlucky. First game of the season at
Elland Road was always going to be tough what with their supporters and all.
"Overall we deserved something out of the game. In anything you do, you need a bit of luck and we didn't get it.
"Decisions went against us and when you get four or five good opportunities away from home you're looking to score at least one of them. I was also disappointed with the goal we conceded."
Leeds: Sullivan, Kelly, Butler, Duberry, Kilgallon, Richardson,
Wright, Walton (Radebe 65), Pugh, Ricketts (Deane 73), Joachim.
Subs Not Used: Carson, Crainey, Guppy.
Goals: Richardson 72.
Derby: Camp, Kenna (Reich 79), Mills, Johnson, Jackson,
Huddlestone (Bolder 61), Taylor, Idiakez, Bisgaard, Smith,
Tudgay (Junior 61).
Subs Not Used: Grant, Peschisolido.
Referee: M Clattenburg (Co Durham).