This was Liverpool's first home fixture since an independent report cleared the club's supporters of any involvement in the deaths of 96 of their fellow fans during the 1989 Hillsborough Stadium disaster.
Uruguay international Suarez, banned for eight games for racially abusing Senegalese-born French international Evra in the equivalent fixture last season, declined to shake the United man's hand before the clubs' last meeting in February.
The two players had been urged to observe the pre-match handshake ritual in a bid to defuse tension among rival fans ahead of Sunday's match and they did so without any fuss.
Ahead of the game both Liverpool manager Brendan Rodgers and United counterpart Sir Alex Ferguson had called on both sets of supporters to refrain from abusive taunting.
In past matches between the clubs, this has seen some of the Merseysiders' fans mock the 1958 Munich air crash which killed several United players.
Meanwhile some United followers, only three days after the publication of the independent report, last Saturday chanted "always the victim, it's never your fault" in their latest attempt to rile Liverpool over Hillsborough.
Prior to Sunday's match, Liverpool captain Steven Gerrard said he hoped Suarez and Evra would observe the pre-match formalities.
"Those two players could be the key," he said. "That's going to be at the beginning of the game, the handshake, and if it goes ahead then they've got a responsibility to start the day off on a good note." – AFP