Vettel managed the rare feat of a fifth-straight race win and leads the championship by 90 points from Alonso with four races remaining. The last driver to win five races in a row was Michael Schumacher in 2004.
Grosjean, who started on the second row, grabbed the lead at the first turn and held it until the 29th lap when he went into the pits for the second time to change tires. Vettel took the lead and waited for his final pit stop on lap 37.
With fresh hard tires, Vettel blasted past Grosjean on lap 41 to take the lead for good.
It was Vettel's fourth win in the past five races at Suzuka. He got off to a rough start when he clipped Lewis Hamilton's right rear tire before Turn 1, forcing the Mercedes driver to retire after the ninth lap due to a puncture and associated damage.
Grosjean was bidding to become the first French driver to win a Grand Prix since Olivier Panis at Monaco in 1996.
Prior to Sunday's race, the drivers honored Maria de Villota with a moment of silence. The former F1 test driver was found dead in a hotel room in Seville, Spain, on Friday. Her family said an autopsy showed that lingering injuries from her racing accident a year ago likely caused her death.