Vettel came from too far back, and clumsily thudded into the side of Verstappen as sparks flew and the Ferrari vehicle spun around.
In a race with Vettel to become just the third driver in history to score as many as five titles, Hamilton can secure the championship in Austin in two weeks' time.
Hamilton held his pole advantage at the start and kept Mercedes team-mate Valtteri Bottas at arm's length throughout the first stint, which was punctuated by a safety auto. Hamilton however has simply gone from strength to strength and once again in Japan demonstrated why the championship is now in his hands.
The timing of Ferrari driver Sebastian Vettel's qualifying run was not as fortunate as he hit a wet patch and spun off the course late in the session qualifying to finish ninth, further damaging his slim chances of catching Hamilton in the championship race.
Raikkonen also felt Verstappen was fully to blame for their tangle, which happened when the Red Bull ran off the road at the chicane on the opening lap while third then banged wheels with the Ferrari as it rejoined.
"When we got to midseason we got that win going into the break and then again, really pushing to make sure that we come back even stronger so again, set the bar high". The German went for a gung-ho lunge on Verstappen as he slowed down from 190mph at the left-handed Spoon corner.
Ferrari, expecting rain, sent Vettel and team mate Kimi Raikkonen out on the intermediate tyres at the start of the final shootout phase of qualifying.
He was penalised five seconds and could well have finished second without it, having crossed the line 1.3 seconds behind Bottas. For me, the gap was there - otherwise I wouldn't do it.
Hamilton was in total control, but while Mercedes looked to be heading to an easy one-two after the pit stops, his team-mate Valtteri Bottas found himself under pressure from Red Bull's Max Verstappen.
"So I don't know why I got a penalty". Brendon Hartley got a bad start and immediately fell down the order while Pierre Gasly's tumble out of the points was drawn out over the whole race.
"He could have been a bit more careful".
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. Races like this are a bit of a hand-over and we know it is hard from where we are in the point standings, but we don't have much to lose.
The "Prancing Horse" hasn't been helped by reports that Team Principal Maurizio Arrivabene could be moving on to Juventus at the end of this season, meaning that a new boss could enter a jaded Ferrari setup.