Kuyt rises above the red mist to floor Everton

Liverpool 1 Everton 0: Dutchman keeps his head in an ill-tempered clash to make it a derby double for improving Liverpool

And this used to be the friendly derby, at least off the pitch. Not any more. A rancorous 213th collision of the Merseyside rivals produced a deserved home win, courtesy of Dirk Kuyt's 50th goal for the Anfield side, but also red cards for Liverpool's Sotirios Kyrgiakos and Steven Pienaar of Everton.

Their dismissals took the total of sendings-off in the fixture since the inception of the Premier League in 1992 to 19, more than any other game. Kyrgiakos' exit left Liverpool to play nearly two-thirds of the match a man short but Everton, who lost Marouane Fellaini on the stretcher after his clash with the Greek defender, never looked capable of exploiting their advantage. Pienaar's banishment in stoppage time merely sealed a wretched afternoon for David Moyes' team.

The three points, secured by Kuyt early in the second half, took Liverpool's tally to 17 out of 21, and in those seven matches only Stoke City, with a scrambled last-gasp equaliser, have beaten Pepe Reina. That the Spanish goalkeeper was scarcely called upon to make a save worthy of the name until the 89th minute, when he dived to tip over Yakubu's shot, was an indictment of an Everton side who had not lost in nine games since a 2-0 defeat in the previous derby.

Liverpool were particularly well served by Jamie Carragher, a boyhood Evertonian, who switched from right-back to central defence following Kyrgiakos' departure. His bone-shuddering but legitimate challenge on Pienaar in the first 10 seconds left the South African nursing a sore shoulder, and possibly a grievance, while reminding colleagues from further afield and with less experience of the fixture what to expect.

Even without three of Rafael Benitez's most creative performers, Fernando Torres, Yossi Benayoun and Glen Johnson, Liverpool had the edge while it was still 11 against 11. Fellaini's ankle injury, which X-rays showed was less serious than first feared, allowed Everton to introduce Mikel Arteta, who has not played a full match for more than a year, but even his dancing feet could not trick them into carving out a clear opening.

Tim Howard had an early warning of the set-piece prowess that would bring Liverpool their winner with a whipped-in free-kick after four minutes that the Everton goalkeeper punched clear with difficulty. Daniel Agger also fired over when well placed, yet the first half rapidly descended into a series of fouls and altercations, with the referee, Martin Atkinson, struggling to maintain control. Liverpool were more sinned against than sinning – there were bad challenges by Leighton Baines on David Ngog and Fellaini on Kuyt – but when Kyrgiakos ploughed into Fellaini with his feet off the ground in the 34th minute, Atkinson issued a straight red. Fellaini had also gone over the top in the tackle but to the Kop's consternation, none of the officials spotted it.

Everton's best chance came late in the first half, when Tim Cahill, whose last eight goals have all been headers, dived to head narrowly over after an untypically intricate move. But the Liverpool 10 were not simply sitting back, and Steven Gerrard, still without a League goal in 2010, clipped Howard's bar from a free-kick. However, when the Liverpool captain swung in a 55th-minute corner, Kuyt, unperturbed by Phil Neville's attempt to pull him back, headed his 10th goal of the season and fourth in derbies.

Fog swirled above the pitch, and as the card count kept rising – it finished on six yellows plus the two reds – Moyes pointed to his watch while Liverpool dug in. Pienaar, fortunate to stay on after a shocking lunge on Javier Mascherano on the half-hour, finally ran out of luck when he jumped into Gerrard and walked a gauntlet of baying Liverpudlians on his way off.

Attendance: 44,316

Referee: Martin Atkinson

Man of the match: Carragher.

Match rating: 7/10