With some 300 metres left the Movistar rider jumped away from the final selection in chase of Dan Martin, made the catch and then outsprinted the Quick-Step Floors's rider at the end of the 258km race from Liège to Ans.
Michal Kwiatkowski (Sky) won the sprint for third ahead of Australia's Michael Matthews (Sunweb) three seconds off the winner.
The day started with a minute's applause in memory of Michele Scarponi, who died on Saturday in a training accident with a van in central Italy, with his Astana team-mates wearing black armbands.
Valverde dedicated the victory and prize money to the Italian rider's family.
“This victory is a tribute to Michele Scarponi, Valverde said. "I was close friends with him and it made me really, really sad to see him go pass away so young, in such tragic circumstances.
"I just couldn't believe it when I saw the news. It wasn't just me, but the whole team, the whole cycling world. All prizes I get here today will go to his family.
The 37-year-old Valverde has won four stage races, the Volta a Catalunya, Vuelta al País Vasco, Ruta del Sol and Vuelta a Murcia already this season, and two one-day classics.
On Wednesday he extended his record of Flèche Wallonne wins to five and has now added a 'Monument' to his season.
Only Eddy Merckx, with five, has won Liège more times than Valverde.
An eight-man breakaway escaped after 7km and opened up a lead of 13 minutes at one stage, Stephane Rossetto (Cofidis) was its final hold-out, caught inside the final 6km.
Further attacks followed before Davide Formolo (Cannondale–Drapac) broke away on his own, as he tired on the final climb up to the finish at Ans, just outside Liege, Martin led the chase.
But the Quick-Step Floors rider slowed after taking the lead and the accelerating Valverde caught him in the final straight before powering clear to win.
"At the final slope in Ans, Martin really went hard to win solo, but I was looking for my distance to sprint, and with 300 meters to go, I just went on full steam to chase him down," Valverde said.
"Even though I saw Albasini sitting on my wheel, I had no doubts about carrying on. I was able to catch Martin, breathe for a few seconds and sprint to the line.
"Because of everything that happened yesterday, it's undoubtedly my most special victory here. I want to thank my whole team, because they were incredible once again, and fulfilled their tasks perfectly so I could focus on pulling this off."
The inaugural edition of a women’s Liège–Bastogne–Liège took place on a 135.5km Bastogne to Ans course, with Anna van der Breggen (Boels–Dolmans) taking her third victory of the week, after claiming the Amstel Gold Race last Sunday and Flèche Wallonne on Wednesday.
With the victory, the Olympic champion made history by becoming the first woman to complete the legendary Ardennes treble.
She finished ahead of team-mate Lizzie Deignan and Kasia Niewiadoma (WM3 Energie) to replicate the podium finishes of Amstel and Flèche.
“I was struggling a lot on the final climb, Côte de Saint Nicolas,” Van der Breggen said. “But I had to launch an attack there and then because, if I had failed to open a gap, it would have made things much easier for my rivals.
“Liège–Bastogne–Liège Femmes is probably the most beautiful race I've ever taken part in. I'm glad to see new races added to the calendar. I still can't believe I've won the treble. It's incredible."
The relentless climbing narrowed the peloton down before Niewiadoma made the first big move.
Going with her were Van der Breggen, Diegnan, Elisa Longo Borghini (Wiggle High5) and Ashleigh Moolman Paiso (Cérvelo-Bigla) while the chase came from a 12-rider group led by Orica-Scott.
The status quo held even as the time gap came down before Saint-Nicolas arrived and Van der Breggen attacked to ride the remaining 7km alone to the finish.
Diegnan and Niewiadoma came through 17 seconds later and Ellen Van Dijk (Sunweb) won the bunch sprint for fourth ahead of Orica-Scott's Annemiek Van Vleuten.
