The Movistar rider will be the hot favourite for Sunday's Liege-Bastogne-Liege, the fourth of five 'Monument' classics on the calendar.
The 36-year-old Valverde, who has won the Tour of Murcia, Tour of Andalusia, Tour of Catalunya and Tour of the Basque Country this year, powered away some 150 metres from the line on the punishing Mur de Huy, a 1.3-km climb averaging 9.3 percent gradient with a passage at 26 percent.
Ireland's Dan Martin was second, one second behind, with Belgian Dylan Teuns taking third place.
France's David Gaudu, at 20 the youngest rider in the bunch, attacked with 250 metres left but Valverde was lying in wait and accelerated shortly afterwards to add a fourth consecutive win to the Fleche title he claimed in 2006.
"The key thing in this race is to be patient," said Valverde.
Gaudu, one of the hottest prospects in cycling, took ninth place.
1 Alejandro Valverde (Spa) Movistar Team 5:15:37
2 Daniel Martin (Irl) Quick-Step Floors 0:00:01
3 Dylan Teuns (Bel) BMC Racing Team
4 Sergio Henao (Col) Team Sky
5 Michael Albasini (Swi) Orica-Scott
6 Warren Barguil (Fra) Team Sunweb
7 Michal Kwiatkowski (Pol) Team Sky
8 Rudy Molard (Fra) FDJ
9 David Gaudu (Fra) FDJ
10 Diego Ulissi (Ita) UAE Team Emirates
Read the original article on Eurosport: Veteran Valverde takes fifth Fleche Wallonne