Starting second on the grid behind polesitter Tadasuke Makino, Lawson passed the Dandelion driver shortly after the pitstop phase to take the lead before marching to a comfortable 4.4s victory.
With Ritomo Miyata finishing only third and Tomoki Nojiri having an uninspiring race en route to eighth, Lawson sits just one point adrift of his TOM'S rivals in the standings with just three races left to run across Motegi and Suzuka.
At the start of the race, Makino fended off a fast-starting Lawson to hold the lead into Turn 1, as Nakajima Racing’s Naoki Yamamoto made a rapid getaway from sixth on the grid to move up to third.
Miyata, the championship leader coming into Fuji, held on to fifth behind the second Nakajima Racing car of Ren Sato, while Nojiri dropped a place to eighth.
In the opening laps, Lawson closed in on Makino on several occasions using the OTS button on the start/finish straight, but the Japanese driver always had the measure of his Mugen rival, as he managed to maintain a one-second buffer up front.
When the pit window opened at the end of lap 10, Sato and Miyata pulled the pin and headed straight to the pitlane at the first opportunity, forcing others to pit as well.
Lawson duly followed the duo into the pits on lap 11, with Makino also getting his mandatory stop out of the way on the following tour.
This proved to be the deciding point of the race as, although Makino was able to hold on to the net lead after completing his pitstop, he couldn’t put up a realistic fight to Lawson on cold tyres.
With Lawson having his tyres up to temperature already, the Mugen driver executed an easy pass on Makino into the Turn 3 left-hander, with the one-time Formula 2 race winner unable to mount any counter-attack.
From there on, the only threat Lawson faced came from Yamamoto, who had decided to go long in the first stint and had the potential to put up a late fight if the safety car came into play.
But such was Lawson's pace on fresh tyres that it soon became clear the Kiwi would have no trouble holding on to his position.
Once Yamamoto and the other late stoppers came into the pits, the way was cleared for Lawson to take a comfortable victory and assert his position as a serious championship challenger.
Makino finished second, marking his second consecutive podium finish, while Miyata completed the podium spots after passing Sato on lap 31 - the move allowing him to hold on to the points lead by the smallest of margins.
Behind, Ryo Hirakawa put in a mighty drive from 20th on the grid to finish fourth, moving inside the top 10 after nine laps before emulating Yamamoto’s strategy and going long in the first stint.
Hirakawa was at one stage over six seconds behind Yamamoto but he had halved the gap by the time the Nakajima driver stopped on lap 25.
The Impul driver stayed out for six more laps and then showed rapid pace on fresh tyres, easing past both Nojiri, Yamamoto and Kakunoshin Ota before passing Sato at the very final corner on the last lap for fourth.
Sato and Ota finished fifth and sixth respectively, the latter scoring his first points of the season, while Yamamoto could only manage seventh having run as high as third early in the race.
Behind Nojiri, the top 10 was completed by KCMG’s Kamui Kobayashi and Inging’s Sena Sakaguchi, both helped by TGM Grand Prix driver Hiroki Otsu bizarrely losing his front-left wheel in the closing stages.
Sakaguchi’s team-mate Sho Tsuboi, another driver in the title fight coming into Fuji, failed to score points after finishing 11th.
