The moment came in a show of unity between the sides at Liverpool's first home game since the Hillsborough Independent Panel's report absolving the club's fans of blame for the 1989 disaster which claimed 96 lives.
Liverpool forward Suarez had refused Evra's hands at a meeting last season, which followed his eight-match ban for racially abusing the Frenchman at a match last October.
The handshakes were part of a pre-match ceremony in which United legend Sir Bobby Charlton presented 96 flowers to former Liverpool star Ian Rush.
Captains Steven Gerrard and Ryan Giggs released 96 balloons, while both sides came out in tracksuits with the number 96 on them.
During the customary pre-match rendition of 'You'll Never Walk Alone', Liverpool fans held up signs spelling out 'Justice' and 'The Truth'.
Both managers had urged restraint from fans at a fixture that has often been marred by a poisonous atmosphere in recent years.
Brendan Rodgers and Sir Alex Ferguson appeared in a joint interview before kick-off, culminating a week of appeals for calm.