Norman Emmerson was also fined £100 after being convicted of using threatening behaviour – but was cleared of a racially aggravated offence.
Emmerson, 33, of Avonmouth Road, Farringdon, had denied both charges.
The court heard he had been arrested at Sunderlands home clash with Middlesbrough in March.
PC Steve Wright told the court Emmerson had been among a crowd of spectators close to the Boro fans, who leapt up when the visitors equalised.
"Once the excitement died down, the defendant remained standing up on his own, directly in front of me," he said.
Emmerson started shouting obscenities and urging the Middlesbrough fans to Come on, before shouting Sieg Heil and making Nazi salutes, said PC Wright:
"I was amazed because it happened so close to me. I went over to the defendant and put my hand on his shoulder.
"He was adamant that he had done nothing wrong and did not know what I was talking about."
PC Sarah Corner told the court she had been standing with PC Wright and had also seen Emmerson abusing visiting fans and making Nazi salutes.
But magistrates agreed to drop the racially aggravated charge after Emmersons solicitor, Paul Heron, argued that it was not legally justified.
"However offensive you may think it could be in a certain context, within the context of the Stadium of Lightfor a person to chant Sieg Heil at a group of Middlesbrough supporters is not a racially aggravated offence, because the visitors are not members of a racial group," he said.
Emmerson denied shouting any abuse at the visiting fans or making any gestures and told the court he had not even been in the ground at the time Middlesbrough scored.
He said he and a friend, Scott Patterson, had slipped into the stadium for the last ten minutes of the game, after the gates were opened to let fans out.