Keane and fellow television pundit Micah Richards were walking to do their post-match analysis when the attack happened, a trial at a London magistrates court heard.
Former Republic of Ireland midfielder Keane was head-butted by Law and fell through some doors in the incident.
Law’s defence team said CCTV footage from inside the stadium showed Keane elbowing the defendant in the face.
Keane, 52, told the court: “I was just walking and, before I knew it, I was hit. I felt the contact and fell back through some doors.
“I was absolutely not expecting it… I was in shock.”
Keane said he suffered bruising on his chest and arms.
Law, who was sat beneath the Sky Sports studio during the match, claimed Keane “picked me out and started telling me to see him outside. He was pointing to doors in the box.”
Law said he went inside the stadium to go to the toilet and encountered Keane who “collided into him”.
Prosecutor Simon Jones KC asked Law: “Are you seriously saying that Roy Keane ran into the top of your head?”
Law said: “I put my head down in a defensive manner to protect my face.”
Jones said Law’s “ridiculous” defence had “changed dramatically” from a prepared statement he gave to police the day after the incident.
Delivering his verdict, District Judge Angus Hamilton said he believed Law had been “untruthful about what happened” during the match and was “sure Mr Law assaulted Mr Keane.”
As well as being barred from attending football matches, Law was ordered to complete 80 hours of unpaid work, and must pay legal costs of £650 ($830) plus a victim surcharge of £114.
© Agence France-Presse
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