The Swedish international stunned the Kop with his first goal for us after 12 minutes of this entertaining clash in the Barclays Premiership.
Andy Reid's attempted cross from the right was deflected all the way to Edman fully 40 yards out. He controlled, steadied himself and let fly into the top corner from 35 yards with Jerzy Dudek only able to look on in disbelief.
It was no less than we deserved after a bright start but Liverpool, still on a high from Wednesday's Champions League triumph against Juventus to set up a semi-final with Chelsea, came firing back.
Luis Garcia equalised with a lovely curling effort just before the break, Robbie Keane headed us back into the lead 10 minutes into the second half only for Steven Gerrard to miss a penalty and then Sami Hyypia to hit a sweet volley from 20 yards to level again.
Liverpool then had the best of it for the final half-hour, Gerrard struck the post with a minute left and Morientes missed from close range in injury time.
But we deserved a point. Edman's goal certainly warranted it, let alone the performances of Michael Dawson and Sean Davis.
Dawson was thrown straight in at the deep end - no reserve football - for his debut after injuries to Noureddine Naybet and Anthony Gardner while Davis was everywhere in his first start since October following knee surgery.
Martin Jol made three changes from the win against Newcastle, Dawson, Davis and Keane in for Defoe.
We started as well away from home as we have all season, Davis and Carrick popping the ball around, Keane and Kanoute's movement causing problems and Dawson settling into defence seamlessly on his debut.
Very little happened in terms of goalmouth incident in the early exchanges but that changed spectacularly after 12 minutes. In all honesty, Keane and Reid's attempt at a short corner went wrong, Reid was closed down as he crossed but the ball went to Edman, fully 40 yards out. He controlled, set himself and lashed it into the top corner with Dudek and the Kop suitably stunned.
It took Liverpool until midway through the half to settle but as Alonso started seeing more of the ball, so the balance of play shifted.
He curled wide after 21 minutes but despite pressing, the home side couldn't crack King and Dawson.
Nunez fired wide as we kept out a succession of Liverpool corners and Robinson had to keep his eye on Gerrard's tricky bouncing volley from 20 yards.
Possession suggested an equaliser might come and come it did with a goal right out of the top drawer just a minute from half-time. Alonso started it by squaring to Gerrard, he rolled it into Garcia who turned and curled beyond Robinson from 25 yards.
One-all at half-time was about right but Robinson made a magnificent save to keep it that way in injury time, somehow blocking Morientes' header from six yards.
Liverpool came out with a spring in their step in the second half but although the home side now bossed possession, there was always a feeling we could score at the other end.
That's just what happened with 55 minutes on the clock as Kanoute fashioned a cross from a tight position on the right flank and Keane rose high to power home his header from 10 yards.
It was end-to-end stuff now and Liverpool came firing back. Gerrard led the way with a burst into the area that was ended as he went over a sea of legs. There were few doubts about the penalty but the Kop gasped again as the skipper drove high and wide with Robinson diving the other way.
Kanoute might have done better from 16 yards but then another fine strike to level matters as Hyypia, of all people, hit a true volley on the full after a corner was half-cleared to him on the edge of the box. It was 2-2, half-hour to go and anyone's game.
This was Liverpool's best spell and they were inches away twice in as many minutes as Garcia lashed wide after a wonderful piece of skill and then Finnan drilled across goal after Nunez and Gerrard opened us up down the right.
Alonso curled just wide but then a host of substitutions disrupted play and that went in our favour.
Hyypia had another volley blocked, Davies forced a fine save from Dudek and then two late scares - Gerrard struck the foot of the post in the 89th minute and then, in injury time, Finnan crossed for Morientes, 10 yards out, only for the striker to blaze over.
GUIDE TO THE ACTION
8mins: Dudek out to gather Kanoute's low cross. Plenty of possession so far, look bright, Dawson looks comfortable, little goalmouth action to report.
12mins: GOAL. Incredible strike from Edman. Ball came out to him from corner, fully 30 yards out, controlled and unleashed shot into top corner with Dudek helpless.
Liverpool 0, Spurs 1
18mins: Lovely move, Davis clipped ball over top to Kanoute, he crossed deep for Carrick who set ball up for Davies but Warnock nipped in to tackle.
21mins: Liverpool also playing decent football, Morientes teed up for Alonso to curl wide of target from 25 yards.
30mins: Davis brilliant sliding block to deny Gerrard thunderbolt free-kick.
33mins: Dawson fine tackle to deny Garcia in box then up to block Gerrard's follow up.
34mins: SUB. Riise for Warnock.
36mins: Nunez did well to fashion shot under pressure but always going wide. Liverpool pressure for the last few minutes, Alonso coming into it more and more.
40mins: Gerrard hit volley into ground from 20 yards, bounced awkwardly for Robinson who gathered well.
44mins: GOAL. More decent Liverpool possession, Alonso to Gerrard, he rolled ball into Garcia who spun and curled into top corner beyond Robinson from 25 yards.
Liverpool 1, Spurs 1
Injury time: SAVE. Morientes header from six yards somehow kept out by Robinson.
Injury time: Keane skied tricky volley into Kop.
Half-time: Liverpool 1, Spurs 1
52mins: CHANCE. Davies skipped around Pellegrino, crossed from right, Reid made move to near post, flick deflected wide by Hyypia.
55mins: GOAL. Kanoute cross from the right, Keane firm header past Dudek from 10 yards.
Liverpool 1, Spurs 2
57mins: PENALTY MISS. Gerrard burst into box, went over a couple of challenges, picked himself up to take spot kick but drove high and wide with Robinson diving the wrong way.
58mins: CHANCE. Straight up the other end, Keane and Kanoute caused panic and Kanoute fired over from 16 yards
63mins: GOAL. Liverpool corner half-cleared, ball fell to Hyypia on edge of box, volleyed on full through bodies and into corner.
Liverpool 2, Spurs 2
67mins: Superb skill from Garcia to beat Carrick in box, had time but lashed over from tight angle.
69mins: CLOSE. Nunez and Gerrard worked an opening for Finnan inside Edman on Liverpool's right, low shot flashed inches wide.
71mins: Alonso curled free-kick a yard wide from edge of box.
71mins: SUB. Ziegler for Reid.
75mins: Block from Dawson as Morientes volleyed Nunez's cross on target.
77mins: SUB. Cisse for Nunez.
84mins: SUB. Biscan for Alonso.
84mins: King there to block as Hyypia let another volley go from 16 yards.
85mins: SAVE. Dudek at full stretch to tip over Davies' curler from 25 yards.
85mins: Kanoute headed Ziegler's cross straight at Dudek.
87mins: CHANCE. Riise cut in from left, fed Garcia 16 yards out, hit shot over.
87mins: SUB. Defoe for Keane.
89mins: WOODWORK. Low Gerrard strike came back off foot of post with Robinson at full stretch.
Injury time: MISS. Finnan cross blasted over by Morientes from 10 yards.
Injury time: Cisse weak shot straight at Robinson.
Full-time: Liverpool 2, Spurs 2
Liverpool: Dudek, Finnan, Carragher, Hyypia, Pellegrino, Gerrard, Garcia, Alonso (Biscan, 84), Nunez (Cisse, 77), Morientes, Warnock (Riise, 34). Subs: Carson, Traore.
Spurs (4-4-2): Robinson; Kelly, Dawson, King, Edman; Davies, Carrick, Davis, Reid (Ziegler, 71); Kanoute, Keane (Defoe, 87). Subs: Cerny, Bunjevcevic, Marney.
FIRST HALF REPORT
Erik Edman's spectacular strike was rewarded with a deserved point in one of our best away performances of the season at Anfield on Saturday.