Liverpool pile more misery on Moyes
The England skipper would have scored Liverpool's first hat-trick at Old Trafford since 1936 if his third penalty had not hit a post after a foul was awarded against Nemanja Vidic for a challenge on Daniel Sturridge.
Vidic was sent off for the tackle - the fourth time he has been dismissed against Liverpool - but replays appeared to show Sturridge had dived to win the spot-kick.
Suarez then rounded off the rout near the end with a well-taken finish.
The scoreline did not flatter Liverpool at all. They thoroughly deserved it.
David Moyes' defence had no answer to the pace of Sturridge and Suarez while their own attack looked completely blunt.
Liverpool's fans rubbed Moyes' nose in it towards the end of the defeat, unfurling a banner that proclaimed the United boss as a 'football genius'.
And for all his public claims that he is the right man to bring the glory days back to Old Trafford, the statistics show how much United have regressed under Moyes' stewardship.
This time last year United were 29 points ahead of Liverpool. They are now 14 behind their bitter rivals with nine matches of the season left.
The 11-point gap to fourth place looks insurmountable while Liverpool's title challenge can no longer be questioned following this momentous result.
With Vidic and Jones at centre-back, United were always going to be vulnerable to the pace of Suarez and Sturridge.
An early warning sign came just two minutes into the game when Sturridge sprinted past Vidic but shot wide.
Suarez was the next to puncture the United defence. He latched onto Jon Flanagan's cutting pass and sprinted into the United box but he inexplicably did not go down when Marouane Fellaini clearly pulled his shorts. Reds boss Brendan Rodgers was up in arms on the touchline.
Liverpool found it easy to open United up with their pace, but the hosts had no such avenue up front.
It was all hit and hope from Moyes' men. Several crosses fell into the Liverpool box but they were all cleared.
Sturridge again got the better of Vidic and Jones with a burst of pace, but he fluffed his shot, and David de Gea made his first save from Allen after Sturridge picked out Suarez in the box.
Flanagan went into the book for his third foul of the afternoon and Rafael soon joined him for a pointless sliding tackle by the corner flag.
Moments later and Rafael handed the Reds the lead. The ball struck the Brazilian's outstretched right hand in his own box as Suarez tried to guide the ball past him and Mark Clattenburg had no option but to award a penalty.
Liverpool argued Rafael should receive a second booking, but Clattenburg did not agree.
Still, the damage had been done and Gerrard made no mistake from the spot, tucking the ball inside De Gea's left-hand post with a precise finish.
United had a strong five-minute spell before the break which involved Wayne Rooney drawing a top save from Simon Mignolet.
United ended the half on the up but just 30 seconds after the restart they imploded.
Guest Diego Maradona and the rest of those in the directors' box were taking their seats when Jones clattered into the back of Allen and the referee pointed to the spot.
Gerrard placed the ball to De Gea's left again before sprinting over to the jubilant Liverpool fans.
Suarez and Sturridge continued to use their pace to good effect. On one occasion the duo came up against five United defenders and they almost scored a third. United's backline was clearly petrified by their pace.
Shouts of 'ole' rang out as the Reds played keep ball while United tried to chase it down.
Robin van Persie, the man who won United the title last year, glanced a free header feebly wide from six yards.
A nightmare afternoon plumbed new depths when Vidic was given a second yellow card for supposedly bringing down Sturridge in the box.
Replays suggested the England striker had dived, and the only crumb of comfort for United was that Gerrard missed his hat-trick opportunity by hitting De Gea's right-hand post.
The fact that Gerrard's miss prompted the biggest cheer of the afternoon from the home fans said it all.
De Gea saved well from Suarez with eight minutes left but the Uruguayan did not miss moments later, latching on to Sturridge's pass to complete a miserable day for United.
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