Liverpool produced a superb display to recover from an early red card for captain Steven Gerrard to beat Everton in a typically fractious Anfield derby that ended with the visitors also down to 10 men.
England midfielder Gerrard was sent off in the 18th minute after a foul, having been booked for kicking the ball away at a free kick 30 seconds earlier, but Liverpool looked the better side from then on and fully deserved the victory against their in-form city rivals.
A Phil Neville own goal and a Luis Garcia lob either side of halftime put Liverpool in control and a superb Harry Kewell strike settled it after the visitors had briefly raised their hopes with a Tim Cahill header before having Andy van der Meyde sent off.
The win takes Liverpool to second place on 64 points, 11 behind Chelsea and one ahead of Manchester United, who have three games in hand, starting with a home game against Birmingham City on Sunday.
"It was a massive achievement not only for us but the fans as well," Kewell told Sky Sports. "It was crucial for us to get the first goal because it's hard to score against 10 men and then we stung them straight after halftime."
Everton had not won at Anfield since 1999 but, coming into the game as the form team of the year, they must have thought this was their day when Gerard was dismissed.
However, after a foul-littered 45 minutes Liverpool took the lead when Alonso whipped in a corner from the right which flew into the net off the head of stretching Everton midfielder Neville.
The depleted hosts made it 2-0 a minute into the second half with a simple goal. A long clearance by goalkeeper Pepe Reina was flicked on by Peter Crouch and as Everton keeper Richard Wright charged from his goal, Garcia was able to calmly lift the ball over him and into the empty net.
Everton grabbed a lifeline after 61 minutes when midfielder Cahill headed in a Leon Osman corner, the goal coming from their first and only real chance of the match. But Liverpool continued to look the better side and Alonso clipped the bar with a free kick and Wright saved well from Kewell.
Everton, who had two men sent off in the home game won 3-1 by Liverpool in December, then levelled the numbers at Anfield when Dutch midfielder Van der Meyde was dismissed for elbowing Alonso five minutes after coming on as a substitute.
Liverpool centre back Sami Hyypia had a 78th minute glancing header ruled out for offside but the frustrated Anfield fans had only six minutes to wait to let rip for real as Kewell unleashed a rising drive from 25 metres.
The goal made it 18 in four games for Liverpool and brought Everton's charge up the table to a halt.
"We didn't play as well as we should have done, we had a great opportunity today," Everton manager David Moyes told Sky Sports. "We had a mad five minutes either side of halftime, really we should have been controlling the game but found ourselves 2-0 down. It wasn't a good day. That period after Steven was sent off was probably our worst part of the game."
