Liverpool had to thank a 44yard free-kick from Gary McAllister three and a half minutes into injury-time for these three points which see them somehow clinging to hopes of a Champions League place after one of the more dramatic Mersey derbies of recent times.
The Anfield club also had their third man sent off in four league games when Igor Biscan trudged away following his second yellow card with 24 minutes remaining. At that moment it seemed that Liverpool would be denied victory in this 164th derby, even though they were 21 up at the time.
Liverpool had taken an early lead early through Emile Heskey and, although Duncan Ferguson equalised before the break, Markus Babbel grabbed his fifth goal of the season to fire the visitors ahead again.
Biscan was dismissed, following on from Danny Murphy and Steven Gerrard in recent weeks, and Liverpool, for whom Robbie Fowler missed a penalty, were hauled level by a penalty from David Unsworth after Ferguson was held by Sami Hyypia.
Everton's tails were up, but, in time added on - after Niclas Alexandersson had fouled Gregory Vignal - up stepped McAllister to unleash his cracker inside Paul Gerrard's right-hand post, though the goalkeeper really should have done better from that distance.
Liverpool, with Thursday's UEFA Cup semi-final secondleg with Barcelona in mind, were without Steven Gerrard, Patrik Berger and the suspended Murphy.
Ipswich's win at Middlesbrough earlier in the day left Liverpool nine points behind them with three games in hand, so anything but a victory for Gerard Houllier's team would surely destroy their Champions League ambitions.
But in the fifth minute Liverpool got the dream start. Dietmar Hamann's quick ball sent Heskey away, Steve Watson played him onside and the striker crashed home his 21st goal of the season.
Liverpool tried to take the sting out of the game with controlled possession play, but, whenever Everton got the ball back, it was soon back in their opponents' box.
This brought its reward in the 41st minute. Campbell won another high ball lofted into the box by Ball and although Jamie Carragher got in a block, the ball spun invitingly into the path of Ferguson who drilled home an equaliser.
The Scot wheeled away waving his shirt over his head and was booked for his troubles.
Everton maintained the abrasive edge after the break but Liverpool broke the stranglehold on 56 minutes.
Hamann flighted a 40-yard pass out to the left for Fowler to scamper away. His cross clipped Ball, then Unsworth, and fell invitingly for Babbel to smash past Paul Gerrard.
Alessandro Pistone took over from the limping Watson after 61 minutes and Alexandersson replaced Gough. After 76 minutes Biscan flew into Unsworth.
Television replays showed he did not make any contact but Jeff Winter was satisfied there was intent and produced a second yellow, and a red.
After 81 minutes Unsworth put his penalty beyond Sander Westerveld and the stage was set for McAllister's finale.
EVERTON: Gerrard, Weir, Gough (Alexandersson 73), Ball, Steve Watson (Pistone 61), Unsworth, Xavier, Nyarko, Gemmill, Campbell, Ferguson. Subs not used: Pembridge, Simonsen, Gravesen. Booked: Ball, Ferguson, Gough, Gerrard, Unsworth, Alexandersson. Goals: Ferguson 42, Unsworth 84 pen.
LIVERPOOL: Westerveld, Babbel, Henchoz, Hyypia, Carragher, Smicer, Hamann, McAllister, Biscan, Heskey, Fowler (Vignal 84). Subs not used: Ziege, Owen, Arphexad, Wright. Sent off: Biscan (77). Booked: Biscan, Hamann, Carragher, McAllister, Henchoz. Goals: Heskey 5, Babbel 57, McAllister 90.
Referee: J Winter (Stockton-on-Tees).
