The Movistar rider bridged to Daniel Moreno (Katusha) to close the gap in the final kilometre and as the fastest rider in the select group did just enough to take a narrow victory.
He finished ahead of Julian Alaphilippe (Etixx-Quickstep) and Joaquim Rodriguez (Katusha) who had latched on to his wheel as he crossed to Moreno.
In a remarkable series of performances over the past eight days the 35-year-old finished second at the Amstel Gold Race and won both the mid-week Flèche Wallonne and Liège.
"It's just unreal," said Valverde. "I'm still not able to realise what I have achieved and I couldn't believe myself when I crossed the line. I knew I was the biggest favourite and everyone was keeping an eye on me at all times, but the team was superb again today - they reacted perfectly in all crucial moments and we were able to win after such a demanding day, so difficult to manage. I was really paying attention to all moves at the front in the finale; I knew Alaphilippe was still there but I wasn't looking only at him, because the group was numerous and any attack could be decisive. Still, huge thumbs up to him - he's done really great and aged only 22, he's performing very high.
"At the slope of Ans, I was seeing Dani Moreno going away. After such a fast, hard race, with all the wear and tear, I knew everyone was going to be tired and also that I was going to struggled to get him back, but I stayed confident he would suffer at the end. I realized he was really going away, wanted to save some energy for the sprint but also knew I had to go after him, so I decided to attack with 600 meters to go to reach him down, but always saving a 'bullet' to sprint at the end, as I did.
"All my three victories here have been beautiful; winning in Liège is phenomenal. However, today's is even more special after such a complete week: second in Amstel, winner in Flèche, winner in Liège. It makes me even happier taking the victory here because of that, doing it in a monument of cycling... and claiming a third one is entering history. I gained strength and confidence through the last few years, and when you're calm and believe in your chances, everything becomes easier. I think this win is a result of that, too."
Exactly 200 riders started in Liège. Ahead was 253km of rolling, punchy terrain with 10 climbs before the grinding finish in Ans.
It took some 30km before eight riders, including Diego Ulissi (Lampre-Merida), Matteo Montaguti (AG2R), Otto Vergaerde (Topsport Vlaanderen-Baloise), Clement Chevrier (IAM), Marco Minnaard (Wanty-Groupe Gobert), Anthony Turgis (Cofidis), Cesare Benedetti (Bora-Argon 18) and Rasmus Quaade (Cult Energy) rode out to a maximum 7min 30sec lead.
From that point the peloton, clearly down to business, got busy bringing them back. The break lost Chevrier, Quaade and Vergaerde with less than 100km to go and with the 70km mark in sight it was over for the leaders.
The speed was high from the start with the peloton averaging over 40km per hour for the first three hours of racing. That pace and the successive climbing ripped the peloton to pieces, particularly on the 3.6km long Côte de Haute-Levée.
Five new riders replaced the previous leaders, Michele Scarponi and Tanel Kangert from Astana, Manuele Boaro (Tinkoff-Saxo), Julian Arredondo (Trek Factory Racing) and Esteban Chaves (Orica-GreenEDGE), clearly intent on setting up the race for their respective team leaders.
At 4.4km long the Col du Rosier proved equally destructive to that group. Arredondo and Boaro tailed off as Scarponi and Kangert set a relentless pace with Chaves a passenger. Ahead? A quartet of shorter climbs but with equal difficulty for tired legs.
With less than 40km left to race the nervousness in the peloton became apparent with a series of crashes which claimed defending champion Simon Gerrans (Orica-GreenEDGE), Nicholas Roche (Sky) and several other riders.
Free of Kangert, Chaves and Scarponi crossed the Côte de la Redoute together with the peloton 30 seconds adrift. But shortly after they too were neutralised.
Sorties were then launched by Roman Kreuziger (Tinkoff-Saxo), Gianpaolo Caruso (Katusha) and Jakob Fuglsang (Astana) as the remaining favourites dodged and weaved with each other.
Repeated attacks from the rear picked up the break before it reached the top of the Côte de Saint-Nicolas with Fuglsang leading.
From there is was every man for himself before Valverde emerged to win the 101st edition of Liège-Bastogne-Liège.
Liège-Bastogne-Liège: 253km, Liège - Ans
1 Alejandro Valverde (ESP) Movistar 6 hr 14min 20sec
2 Julian Alaphilippe (FRA) Etixx-QuickStep
3 Joaquim Rodriguez (ESP) Katusha
4 Rui Costa (POR) Lampre-Merida
5 Roman Kreuziger (CZE) Tinkoff-Saxo
6 Romain Bardet (FRA) AG2R
7 Sergio Luis Henao (COL) Sky
8 Domenico Pozzovivo (ITA) AG2R
9 Jakob Fuglsang (DEN) Astana
10 Daniel Moreno Fernandez (ESP) Katusha