Deceuninck-QuickStep's Alaphilippe kept his powder dry before putting in a blistering attack in the closing hundred metres to keep out Astana's Fuglsang – his regular sparring partner – by less than a bike length after the pair had ridden clear of the field on the mythical uphill finish.
WATCH - Alaphilippe takes victory in dramatic Fleche Wallonne finish
Italy's Diego Ulissi (UAE Team Emirates) came home six seconds later for third place before Belgium's Bjorn Lambrecht (Lotto Soudal) and Germany's Max Schachmann (Bora-Hansgrohe) completed the top five.
Despite being present in the main pack ahead of the decisive climb, there was no historic sixth win – or even a top ten finish – for veteran world champion Alejandro Valverde (Movistar), whose eleventh place was his worst showing in La Flèche Wallonne since returning from a doping ban in 2012.
Alaphilippe's latest victory was his ninth so far in a stellar season that has also seen him win Milano-Sanremo and Strade Bianche. It was his QuickStep team's 25th of the campaign.
"This race is something special for me as I always seem to finish on the podium whenever I come here," said 26-year-old Alaphilippe, who twice finished runner-up to Valverde before winning his first Flèche crown last year.
Alaphilippe - This is a special race for me
"I've won a lot this year, many victories and I always like to do something and today at La Flèche Wallonne I've done it.
"I'd like to thank everyone on the team, they've been phenomenal, the staff as well. This part of the season, this Classics part of the season, is something I love and I'm grateful to give it to the team."
Alaphilippe paid tribute to team-mates Dries Devenyns and Enric Mas, who worked tirelessly for the Frenchman after he picked up a puncture in the closing 50km of the 195km race, as well as the man he beat.
"I need to pay tribute to Jakob Fuglsang," Alaphilippe said. "He's a big man and of course he'll be very disappointed like I was after Amstel Gold. Today we finished first and second, up front together like we did in Strade Bianche."
Alaphilippe's pound of Flèche: how it happened
A five-man break formed within 20km of the start in Ans featuring Dutchman Koen Bouwman (Team Jumbo-Visma), Americans Joey Rosskopf (CCC Team) and Robin Carpenter (Rally UHC Cycling), Luxembourg's Tom Wirtgen (Wallonie Bruxelles) and Dutchman Kenneth Van Rooy (Sport Vlaanderen-Baloise).
The leaders built up an advantage of five minutes over the peloton before hitting the business end of the race: three laps of a new 29-kilometre finishing circuit boasting the ascents of the Côte d’Ereffe, Côte de Cherave and the Mur de Huy.
Moments after the Netherland's Anna van der Breggen won for a fifth consecutive time on the Mur de Huy in the women's race, the break in the men's splintered with Van Rooy and then Wirtgen slipping off the back.
With nine climbs in the final 77km, the new configuration of the race was always going to spice things up – and so it proved as numerous attempts to bridge over ensued, with Australia's Nathan Haas (Katusha Alpecin) particularly active and former world champion Peter Sagan (Bora Hansgrohe) quickly distanced.
Bouwman, Rosskopf and Carpenter held a gap of 2'40" going over the summit of the Mur de Huy for the first time with 57km remaining as QuickStep set tempo behind.
Quick change for Alaphilippe after puncture
Alaphilippe punctured with 43km remaining before two large crashes in the nervous peloton ended the hopes of some big-name riders, including Briton's Adam Yates (Mitchelton-Scott), Italy's Domenico Pozzovivo (Bahrain Merida) and the Spaniard Ion Izagirre (Astana).
The remaining three leaders were swept up on the second ascent of the Mur de Huy as a dangerous group of riders went clear following an attack by Italian Giulio Ciccone (Trek Segafredo).
It was left to the Movistar team of five-time winner Valverde to close the gap before Poland's Tomasz Marczynski (Lotto Soudal) put in an attack with 20km remaining on the Cote d'Ereffe. The Pole was shortly joined by Slovenia's Matej Mohoric (Bahrain Merida) but they never had more than 15 seconds to play with.
Behind, it was QuickStep's Devenyns who led the chase before the race came back together on the Cote de Cherave with 7km remaining. Mas then came to the front to set a furious tempo that whittled down the pack ahead of the finale.
When the Mur de Huy came it was Team Sky's Wout Poels who led team-mate Michal Kwiatkowski onto the climb in pole position – and when it came to the steepest part of the double-digit ramp, it looked like Amstel Gold all over again as Kwiatkowski, Fuglsang and Alaphilippe came to the fore.
Fuglsang made his move on the infamous hairpin bend with 500m remaining with only Alaphilippe able to bridge over. The Frenchman then shadowed the Dane before putting in his killer blow with 100m remaining.
But it wasn't quite over yet: a late surge by Fuglsang forced Alaphilippe to dig deep and, weaving across the road to close the door on his rival, the most consistent man of the entire classics campaign secured his successive win in La Flèche Wallonne.
After coming second in Brabantse Pijl, fourth at Amstel Gold and now first in La Flèche, Alaphilippe will be odds-on favourite to end the so-called "Ardennes Week" on a high by becoming the first Frenchman since Bernard Hinault in 1980 to win Sunday's Liège-Bastogne-Liège. On this form, few can stop him.