Bouncing back from their failure to finish at Le Mans that so severely dented their title chances, the polesitters delivered a controlled victory aboard the #7 Toyota GR010 HYBRID Le Mans Hypercar.
A race that featured three safety cars meant their advantage was just 16 seconds over the #50 Ferrari 499P LMH of Miguel Molina, Nicklas Nielsen and Antonio Fuoco, but the Toyota had looked comfortable since Lopez took over in the lead during the middle portion of the race.
Conway led the early laps until he was ambushed following the first safety car by an inspired Mikkel Jensen in the #93 Peugeot 9X8 LMH.
Molina then followed through on Conway, who also fell behind Michael Christensen's #5 works Porsche 963 LMDh during the second stint as Jensen fell back, but the Toyota's long run pace brought him right back onto the tail of the leading Ferrari after Christensen pitted.
Lopez emerged ahead of Nielsen following their second stops and the car was never headed outside of the pit cycles thereafter, with Kobayashi able to edge away from Fuoco after the advantage north of 46 seconds was wiped out by the final safety car.
This was called when Harry Tincknell stopped on track in the Proton Competition Porsche, making its WEC series debut, which had led at stages through the pitstop cycles.
The #93 Peugeot recorded the French marque's first WEC podium with Jensen joined by Jean-Eric Vergne and Paul di Resta following a clean run, one year on from the car's first outing at Monza.
The #8 Toyota of Sebastien Buemi, Ryo Hirakawa and Brendon Hartley recovered to finish fourth after it was delayed by two penalties. It incurred 10s at the car's first pitstop when Buemi tapped Antonio Giovinazzi's #51 into a spin at the race's first corner, then copped a 60s stop-go for glancing side-on contact with Satoshi Hoshino's D'Station Aston Martin Vantage GTE that sent the Japanese heavily into the barriers at Ascari.
This prompted a strategic split between cars that pitted under the first safety car and those that stayed out. Those that went with the former were then hampered by the second safety car, the result of Gabriel Aubry's Vector ORECA-Gibson 07 being spun into the wall on the exit of Lesmo 2 by LMP2 rival Bent Viscaal (Prema), which meant they had to stop for emergency service then pit again when the race went green.
Among those delayed was the recovering #51 Ferrari that finished fifth on the road in the hands of Giovinazzi, Alessandro Pier Guidi and James Calado.
The Briton passed the #5 Porsche Christensen shared with Dane Cameron and Fred Makowiecki shortly after Hartley in the final 15 minutes of the race, but was demoted back behind it by a 45-second post-race penalty applied for overtaking outside of the circuit limits on the straight.
The second Penske Porsche of Kevin Estre, Andre Lotterer and Laurens Vanthoor was another hampered by the need to take emergency service and ended up seventh, serving a late drive-through penalty for overtaking under the safety car, ahead of the Glickenhaus-Pipo 007 of Olivier Pla, Nathaniel Berthon and Romain Dumas.
The top 10 was completed by two other cars that were made to pay for adopting the early pitstop strategy, the privateer Jota-run Porsche and the sole Cadillac V-Series.R fielded by Chip Ganassi Racing.
Jota did however claim its first LMP2 victory of the season with Pietro Fittipaldi, Oliver Rasmussen and David Heinemeier-Hansson. The British crew, and WRT's similar #31 ORECA, crucially stopped just before a VSC initially triggered for Tincknell's stoppage that became a full safety car.
That meant their nearest rivals, the #23 United Autosports ORECA, had to wait until the race went green again before stopping, while WRT's #41 car had to take emergency service before doing likewise.
WRT's Robin Frijns, therefore, led Fittipaldi until the final stops, when a longer fill for the Dutchman put Jota into a lead it held until the end with a margin of 36.220s.
A late retirement for the car shared by Frijns, Ferdinand Habsburg and Sean Gelael, which faced a potential penalty for Habsburg overtaking the eventual race-winning Toyota under FCY, elevated the #36 Signatech Alpine crew of Charles Milesi, Matthieu Vaxiviere and Julien Canal to a first podium finish of the season.
The #41 WRT entry of Louis Deletraz, Robert Kubica and Rui Andrade finished third after Deletraz passed Oliver Jarvis's United Autosports machine at the second chicane, both running off the track as the Swiss moved alongside on the outside line.
Corvette Racing drivers Nicky Catsburg, Nico Varrone and Ben Keating sealed the GTE Am drivers championship despite only finishing fourth, as Porsche locked out the top three positions.
A canny strategy helped Dempsey Proton Racing drivers Julien Andlauer, Mikkel Pedersen and team boss Christian Ried to secure their first win of the season aboard the #77 Porsche 911 RSR-19.
The #77 Porsche 911 RSR-19 crew made one fewer pitstop than their rivals to beat the #60 Iron Lynx Porsche of Matteo Cressoni, Alessio Picariello and Claudio Schiavoni by 11.184 seconds.
The #86 GR Racing Porsche driven by Ben Barker, Riccardo Pera and Mike Wainwright completed the Porsche podium lockout as Corvette had to settle for fourth after a drive-through penalty when Varrone sped in the pits.
However its points advantage after wins at Sebring, Portimao and the double points Le Mans 24 Hours put it beyond reach of the Iron Dames Porsche that finished fifth with only two rounds of the season remaining.