Verstappen left minimal room and Vettel clattered into the Red Bull, spinning himself to the back of the field and sustaining sidepod damage.
Mercedes driver Hamilton extended his advantage at the top of the standings to 67 points with his fourth successive race win and sixth in seven, with team-mate Valtteri Bottas taking second ahead of Red Bull's Max Verstappen.
Vettel trails Hamilton by 50 points with only four races to go after Sunday's Japanese round. He was quick off the line and had passed the Toro Rosso's of Pierre Gasly and Brendon Hartley by the time he was into the esses to take sixth and the Haas of Romain Grosjean fell swiftly afterwards.More news: Manchester United 3-2 Newcastle: THINGS YOU MISSED
There was a short safety-car intervention to clear up debris left by a collision between Kevin Magnussen's Haas and Charles Leclerc's Sauber and bodywork strewn around the lap by the Dane as he returned to the pits with a puncture.
Vettel managed one run on slicks between pitting to get rid of intermediates and the rain coming back, but ran off-track at Spoon. The Ferrari was mostly alongside entering the corner, only for the two to collide. "Tomorrow is a new day".
Verstappen had already incurred a five-second penalty after nudging Kimi Raikkonen's Ferrari off the track.
After a virtual safety vehicle, called after Leclerc pulled off with a mechanical failure, Bottas began to run into blistering problems with his tyres.More news: Gary Neville blasts Manchester United hierarchy amid Jose Mourinho reports
Verstappen finished third and Australia's Daniel Ricciardo was fourth behind his Red Bull teammate, after starting 15th on the grid.
As a season that began with such promise appeared to be on the brink of collapse, Vettel admitted Ferrari had been under pressure to come up with something special at Suzuka. Verstappen was hugely impressive - but loses marks for his incident with Raikkonen and the attitude he showed by saying on the radio the Finn "could have waited for me". Judgement reservedWhat happen next?
He finished 11th in the race on that occasion, unable to better the 10th-place finishes he had at the Azerbaijan and German Grands Prix this year. He's going to do it soon. "Obviously, I had a mistake at Spoon so I lost most of the time there but obviously the second run we didn't make it out on time because the rain came".
Hamilton secured the 80th pole position of his F1 career at Suzuka in a tricky Q3 session where changeable conditions gave teams timing and tyre choice headaches.More news: Senators Collins, Manchin back Kavanaugh, paving way for confirmation
In the first instance, Verstappen was given a 5-second time penalty and a single penalty point on his license as the stewards had ruled that he had "cut the chicane and rejoined track on the racing line in turn 17 and in the process collided with auto 7".