Vettel jumped from eighth on the grid to fourth at the end of the opening lap - which concluded under safety auto conditions - but the restart would ultimately be ruinous for the Ferrari.
That means Hamilton only needs to outscore Vettel by eight points at the next race in the United States to clinch a fifth world championship.
Daniel Ricciardo carries an image of a Honey Badger on his helmet because he identifies with the animal's strength, ferocity and fearlessness.
After the restart, Vettel was behind Verstappen and he saw an opportunity to pass into Spoon when the Red Bull slowed approaching the corner as the engine went into energy harvesting mode.
Kevin Magnussen's Haas picked up a puncture after he moved to the right down the start-finish straight defending from Charles Leclerc and was rear-ended by the Sauber.
"When you get in the vehicle it's just the best, it's so much fun and I'm truly grateful to have the opportunity I have".
Haas trimmed Renault's advantage in the constructors' championship to 11 points in Russian Federation, but they could nearly erase the deficit altogether with a strong result in Suzuka. Race winners get 25 points.
Stewards reviewed the incident and chose to take no further action.
Only three cars retired from the grand prix - Magnussen, Leclerc, who had also been rear-ended by team-mate Marcus Ericsson just as they prepared for the restart after the safety vehicle, and Renault's Nico Hulkenberg. Instead, they have a home crowd to please for power unit partner Honda.
The rain and sunshine mixed to create a pretty sight in the sky. But during that excitement, Mercedes calmly made their way into the top 10 shoot-out using the soft compound tyre, compared to rivals Ferrari and Red Bull who opted to advance on the supersofts.
"I have raced a long, long time, but the happiness I have inside is as high as always so it is a great feeling".
Unfortunately, his hopes of improving on his first run - and possibly stealing pole position from Hamilton for the second race in succession - were thwarted when the rain picked up again.
Despite only a smattering of raindrops in the moments before the shootout for pole, Ferrari elected to put Vettel on wet tyres.
"I do not think that pole position was within our reach, but what happened today is unacceptable", Arrivabene told Motorsport.com.
The Dutchman served a five-second time penalty for leaving the track and not returning safely, forcing Raikkonen onto the grass after overrunning a chicane. Vettel and Kimi Raikkonen, meanwhile, were sent out on intermediates at the start of Q3 in anticipation of the rain coming earlier.