The United captain reacted angrily by grabbing the arm of the Uruguayan as he walked straight past the left-back. Further down the line Rio Ferdinand then turned the tables by not offering his hand out to the South American.
This prompted boos from the United fans when Suarez touched the ball with the away supporters jeering when Evra had possession.
Tensions escalated further during the half-time break when the Frenchman tried to talk to the Liverpool man but Martin Skrtel got between the players and a brawl broke out, according to Sky Sports.
Red Devils' boss Sir Alex Ferguson could not hold back his anger at the opposing player's decision and told Sky Sports after the match: "I couldn't believe it. I just could not believe it.
"I had a chat with Patrice this morning, and he said 'I'm going to shake his hand. I've got nothing to be ashamed of and I want to keep my dignity.' And then he [Suarez] refuses - he's a disgrace to Liverpool Football Club.
"That certain player should not be allowed to play for Liverpool again. With the history that club has got, and he does that in this city today - he could have caused a riot.'"
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