World champion Hamilton, who leads the championship standings by 41 points from Rosberg, will start alongside the German at Suzuka on Sunday, while Ferrari's Sebastian Vettel qualified for the second row.
"Happy birthday, mum!" Rosberg said in German after securing only his second pole of the year.
"That's a birthday present for you. At times today I had the perfect car and I pretty much nailed my laps. Obviously it's a great comeback for the team after Singapore."
Rosberg also topped the timesheets in a frantic final practice session on Saturday morning after heavy rain effectively washed out Friday's practice.
With memories of Frenchman Jules Bianchi's fatal crash at Suzuka last year raw this weekend, Kvyat reminded everyone of Formula One's inherent risks when he crashed spectacularly on approach to the hairpin.
Despite flipping over and totalling his car, the Russian was able to climb out of the mangled wreckage unhurt as red flags brought a premature end to qualifying.
The Dutch teenager trudged back to the pits, yellow flags having bounced out several drivers, including Jenson Button, who was furious after his worst ever Japan qualifying result.
Race stewards subsequently demoted Verstappen. "The position we are in, we can't afford to make any mistakes," the Englishman snapped at McLaren mechanics, referring to a communication mix-up.
Red Bull's Daniel Ricciardo qualified seventh quickest with Frenchman Romain Grosjean alongside him on the fourth row for the troubled Lotus team, whose Formula One future has been plunged into doubt over a cash-flow crisis.
