The Ferrari downfall coincides with the appointment of Sebastian Vettel in 2015 after the German won four straight Championships with Red Bull from 2010-13 in a supremely fast vehicle under the guidance of race engineer Adrian Newey.
That puts Vettel 67 points behind Hamilton and means the Briton would win the title at the US Grand Prix in Austin, Texas, in two weeks' time if Mercedes finish one-two for the third successive race.
Suzuka - Sebastian Vettel has refused to point fingers after Ferrari calamitously chose the wrong tyres in Japanese Grand Prix qualifying on Saturday. 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.
"Austin is generally a good track for us and I can't wait to unleash this beast there", said Hamilton after leading every lap from pole position.
Verstappen went on to finish third regardless, and when told by team principal Christian Horner after the race that he would not be "too popular with Ferrari and the Italians", he jovially replied: "That's not my problem, they were too aggressive".
Despite the mistakes and a heavy points loss in both championships, Vettel said that seeing the team work was "inspirational" and claims the team doesn't have much to lose now with four races to go.
Raikkonen tried to clear him round the outside of the second part of the chicane, only to be forced off by the rejoining Red Bull and fall behind Vettel.
"I think it's correct that maybe we've been on the wrong side a couple of times but I don't think there was an bad big gap or an bad lot to get wrong".
One once 50 point gap has now increased to 67 after Vettel made an ambitious pass on Verstappen on Lap 10 at the Spoon.
India vs West Indies live scores first Test day three
Asked if it was the team's plan to attack the spinners and try to unsettle them, the opening batsman played it down. By pulling its biggest ever Test win over West Indies , India took a 1-0 lead in the two-Test match series.
Before the Vettel collision, Verstappen had already had an incident with the other Ferrari of Kimi Raikkonen and been given a five-second time penalty to serve at his pitstop.
"I knew he had a penalty but I also felt that we were faster".
Valtteri Bottas held off Verstappen to take second nearly 13 seconds behind Hamilton in a breathless 53-lap race at the fast-flowing Japanese circuit.
"He could have been a bit more careful".
Vettel's move smelt of desperation, and it marked his seventh mistake of an increasingly-erratic campaign which has unravelled since the summer break.
Asked who made the decision, he said: "Does it matter? I am just grateful to have delivered".
"He ran wide and went off the track and I just went on the outside at the next corner, leaving him space", growled the Finn, who finished fifth.
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.