The diminutive forward, who became the most expensive Japanese player when he moved to Al-Duhail in January, scored the winner in the 76th minute having come off the bench 15 minutes earlier.
Japan coach Hajime Moriyasu made a swathe of changes after his side's loss in another friendly against South American opposition last Friday, when they played Colombia, including bringing Shinji Kagawa back into the starting line-up.
But the new players struggled to take advantage of their overwhelming possession until Moriyasu made his second half changes.
The three attacking substitutes - and usually Moriyasu's favoured forward line - of Ritsu Doan, Takumi Minamino and Nakajima combined finally to unlock the Bolivian defence and give the Samurai Blue a morale-boosting win.
Japan have used the friendlies as preparation for the Copa America beginning in Brazil in June, which they have been invited to play in along with Qatar.
Japan, the Asian Cup runners-up, have now played 14 games since the Russia 2018 World Cup and have only lost twice under Moriyasu.
Bolivia, meanwhile are on a miserable run, having failed to win since a 3-0 victory over Myanmar in October. They begin their Copa campaign against hosts Brazil on June 15.
(Reporting by Jack Tarrant; Editing by Hugh Lawson)
