On his first start since serving an eight-match ban for racially abusing Evra at Anfield in October, Suarez refused to offer his hand during the traditional pre-match handshake.
Evra reacted angrily and after apparently trying to confront Suarez in the tunnel at the end of the first half celebrated victory in close proximity to a disconsolate Suarez.
The Uruguayan continued to walk down the tunnel as some of Liverpool's players took umbrage at Evra's celebrations, remonstrating with the defender as tempers threatened to boil over.
Rio Ferdinand had earlier refused to shake Suarez's hand either, emphasising the depth of his feeling at recent events.
Amid the rancour, United emerged with three precious points as Wayne Rooney's second-half double sent them top of the Premier League.
Sir Alex Ferguson's men had to survive a nervy 10 minutes at the end though after Suarez's close-range finished had halved the deficit.
Reaction to Suarez was swift and damning and Evra was so obviously not amused.
Ferdinand might not have thought so, but it was probably just as well he bore the brunt of Evra's intended challenge on Suarez inside the first minute, otherwise the United skipper would have been in trouble.
Nothing much happened for a long time after that, with the game getting stuck in a midfield scrap.
Glen Johnson had the clearest opportunity, only to curl his shot wide after skipping inside Evra.
Rafael responded with a similar opportunity, which was saved by Pepe Reina.
It was not long before United opened their visitors up though.
Paul Scholes continued his run after finding Ryan Giggs with a quite brilliant pass to the left touchline.
When Giggs delivered the cross, Scholes was all on his own on the edge of the six-yard box.
It should have been the opener. Instead, the veteran midfielder's header went straight at Reina, who batted it away.
After the flurry of activity, the contest reverted back to the mundane.
That was until the final minute of the half, when Ferdinand sent Suarez to the deck with a tackle TV replays showed was perfectly legal.
Suarez felt differently and when referee Phil Dowd refused to award the free-kick that would surely have brought Ferdinand's dismissal, he reacted furiously.
Booting the ball at towards the dug-out as the half-time whistle blew, Suarez had to be escorted down the tunnel by team-mates.
Once inside though, the whole thing exploded once more, with Evra apparently intent on confronting the Uruguayan, with players from both sides involved in a melee that required police intervention.
The Football Association will be wanting to know more about that but the spark suited United better judging by the way they began the second half.
When Jordan Henderson could only get the faintest of touches to Giggs' curling corner, it sent the ball straight to Rooney.
On his own at the far post, the England striker swept home a first-time shot.
The home fans barely had time to catch their breath before Rooney struck again.
This time, Liverpool only had themselves to blame as Jay Spearing surrendered possession to Valencia in a dangerous area.
Unselfishly, Valencia found Rooney immediately and the United man finished off his 17th Premier League goal of the season.
The whole complexion of the afternoon had changed.
After Michael Carrick had sent Suarez flying, Rooney was denied a hat-trick when he brilliant effort was ruled out for an earlier foul by Jonny Evans.
More good work from Valencia presented Rooney with another opportunity, which he spurned.
It triggered a double substitution from Kenny Dalglish, who introduced Andy Carroll and Craig Bellamy.
Then, after Danny Welbeck had scuffed a shot straight to Reina, Charlie Adam came on.
Suarez remained throughout, so was on hand to finish off after United's defence had got themselves in a tangle as they tried to clear Adam's free-kick and the ball bounced kindly off Ferdinand.
Welbeck would have eased a few nerves if he had not wasted a good chance on United's next attack.
However, after an excellent save from David de Gea to deny Johnson in stoppage time and Suarez missing from close range when he was offside anyway, the hosts held on to claim a valuable win, even if the hope of both clubs that the match should remembered for the football was sadly not met.