Liverpool 4 Everton 0: match report These are increasingly exciting times for Liverpool, who are clearly responding strongly to Rodgers" enlightened, attack-minded management. Victory gives Liverpool their best goal difference (+29) after 23 games of a Premier League season, eclipsing their totals in 1994-95 and 1995-96. Victory also gives Liverpool what Rodgers called "bragging rights" in local arguments and "vital points" in the chase for Champions League football. Everton never gave up, and Kevin Mirallas was always a threat, but this was painful for their fans to watch, their mood darkened further by an ankle injury suffered by Romelu Lukaku, who left the field on a stretcher and the ground with his ankle in a cast. Everton will assess possible ligament damage today. As if to accentuate Everton's misery, Lukaku sustained the injury colliding with Gareth Barry as Liverpool scored their first. Any hope that Everton would be lifted by the quick return of Ross Barkley from a broken toe soon dissolved as Liverpool, so quick in mind and movement, dominated this 222nd Merseyside Derby, the 190th league meeting between the rivals. Badly missing Sylvain Distin and Seamus Coleman, Everton were too naïve at the back. Liverpool were too fast, too determined, too alive to the visitors" vulnerability. Barring an early long-range strike from Barkley into the Kop, Liverpool settled far the swifter. Tim Howard's goal came under immediate pressure, the keeper denying Jordan Henderson and Suárez. James McCarthy and Barry tried to shield Everton's weakened back-four but were kept constantly busy by the movement of Suárez and Coutinho. Suárez was roaming all over, a fox hunting easy pickings, occasionally shifting wide to examine John Stones" capabilities and also switching with Sturridge in the centre. Trying to contain Suárez was like trying to pin mercury to a wall; he was too elusive. With Gerrard delivering some low, pinpoint passes skidding across the glistening canvas to Suarez and company, Everton were under extreme pressure, struggling to get the ball. They did have a chance, a skewed shot from Steven Pienaar, but this was the Liverpool show, the Gerrard show, the Sturridge show, the Suarez show. Howard thwarted Suárez, then Sterling, before Liverpool broke through after 21 minutes. When the persistent Suárez won a corner in front of the Everton fans, the Uruguayan appeared to have a couple of missiles thrown at him. Suárez jogged over to the corner flag, ignored the Everton fans, focusing on the ball, running in and sending it towards the near-post where the unmarked Gerrard, darting from right to left, powered his header in. It looked a goal made at Melwood. As Liverpool celebrated, the Everton medical staff came on to attend to Lukaku, who was lying on the ground, having turned his ankle when bumping into Barry. Eventually lifted on to a stretcher, Lukaku was carried away, the striker holding his hands to his face. Steven Naismith ran on, attempting vainfully to replace Lukaku. Already trailing, the sight of Lukaku departing further drained some of the belief from Everton. Liverpool went for the jugular again after 32 minutes, this time scoring from a magnificent flowing move, a break full of touch and speed. Coutinho angled his pass from right to left towards Sturridge. Only when Coutinho had released the ball did Stones spot Sturridge's run. Too late. Sturridge controlled the speeding ball with his left foot, and then despatched it unerringly past Howard. Everton's defence were shellshocked, utterly failing to respond when Liverpool came raiding again three minutes later. Kolo Touré hooked a clearance upfield, and only Sturridge realised its possibilities. Noting Howard advancing out, Sturridge calmly lobbed the ball over him. It went high and then dropped almost arrogantly over the line. Everton tried to respond. Jagielka and Barry went close. Barkley had a shot blocked. The excellent Mirallas kept looking for little glimpses of space in Liverpool's defence but Touré and Martin Skrtel held firm. Liverpool added their fourth five minutes into the second half, Suárez racing away from Jagielka and slotting the ball past Howard. Four minutes later it should have been 5-0. When Howard brought down the flying Sterling, Gerrard generously offered Sturridge his hat-trick chance but he skied the penalty.