There was an increased police presence in Sheffield for the match, which attracted a crowd of 23,909 for the 12.30pm kick off.
South Yorkshire Police said although there were a few incidents involving a small minority, the majority of the fans were there to enjoy the game, which Leeds lost 2-0.
One person was arrested in the ground for criminal damage and another person was arrested after the match for a public order offence.
Eight Section 35 dispersal notices were issued to fans in Sheffield city centre before the game.
Supt Scott Green, who was overseeing policing of the match, said: “I’d like to thank the majority of fans for their co-operation at today’s match.
“We had a high-profile presence in Sheffield city centre and at Hillsborough, to ensure the safety of supporters and minimise disruption to other members of the public going about their daily business.
“The majority of the fans were there to enjoy the game and I’d like to thank these fans for ensuring the match was a safe and enjoyable game for everyone.”