The runaway Asian Group C leaders failed to sparkle on a chilly night in Saitama until Crystal Palace forward Kamada pounced for the opener in the 66th minute.
Kubo added another in the 87th minute as Japan punched their ticket to next year's tournament in the United States, Canada and Mexico.
It will be their eighth straight World Cup appearance.
"I'm relieved that we could qualify at home in front of our supporters," said Kubo, before he and his teammates doused coach Hajime Moriyasu with water.
"This here is not our goal - we want to compete against strong teams at the World Cup."
Australia's 5-1 home win over Indonesia earlier in the evening meant Japan would have clinched their place even with a draw.
But Kamada made sure they did it in style in front of an expectant crowd of just under 60,000.
He latched onto Kubo's reverse pass and dispatched the ball past Bahrain goalkeeper Ebrahim Lutfalla just three minutes after coming on as a substitute.
Real Sociedad's Kubo added some extra gloss to the night with a left-footed shot from a tight angle.
Japan's players sprinted onto the pitch at the final whistle and celebrated with the home supporters.
Japan have been in unstoppable form in the Asian third round of qualifiers and went into the game having won five and drawn one of their games so far.
Coach Hajime Moriyasu started with an experienced lineup featuring Premier League talent in Liverpool's Wataru Endo and Brighton's Kaoru Mitoma.
Captain Endo thought he had given his team the lead in the ninth minute when he rammed home a loose ball in the box, only for the goal to be disallowed by VAR.
Japan continued to press for the opener but Bahrain had several dangerous raids on the counterattack and Komail Al Aswad should have done better just after the half-hour mark.
Japan were also wasteful and Mitoma blazed over the bar with the goal at his mercy in first-half injury time.
Moriyasu shuffled his pack midway through the second half, bringing on Kamada and Junya Ito for Takumi Minamino and Ritsu Doan.
The impact was immediate as Kamada gave Japan the lead with his ninth goal for his country.
Kubo went close to adding another with a curling shot that Lutfalla clawed away with five minutes remaining.
But the attacker got his goal with time running out as Japan made sure of the win, and with it a place in North America.