The triple champion heads to the Suzuka circuit having extended his overall lead over Vettel to 34 points in the standings with just five races to go.
Hamilton was able to find yet more time in Q3, putting him over 1.5 seconds clear of Schumacher's best time from 2006.
He switched to the new package for Friday practice at Suzuka and, after finishing second behind Sebastian Vettel in a dry first practice, he said his auto felt competitive again.
Mercedes technical chief James Allison acknowledged the auto could be "difficult", adding "we would like a vehicle that is easier to throw at the race track".
"It's been an interesting day". A small duck also got far too much airtime at this point, indicating that what we really needed was some cars on track! I believe we have a strong auto and there are plenty of races left. After both cars got their laps done, and a feel for high and low fuel, he said the team were "reasonably pleased with the initial balance and performance".
Ferrari endured a torrid September, suffering a double first-lap DNF in Singapore and then race-wrecking engine problems in Malaysia.
"That's what I try and do, make sure every weekend I'm the best prepared I can be".
The Spaniard, though, went into qualifying with a 35-place grid penalty after his team installed a fresh Honda power unit in his vehicle overnight, exceeding his permitted allocation for the season.
"Our pace was pretty good, but we still need to find a good compromise with the downforce we are going to run here", the Australian said. Otherwise, given the pace we've seen from Hamilton and Mercedes this weekend, the No.44 auto could disappear into the distance if he leads into Turn 1.
When the cars did finally creep out, puddles made the going treacherous but Lewis steered his Mercedes to the quickest time of one minute, 48.719 seconds.
Teams were reluctant to run because each driver is limited to four sets of wet-weather tyres for the weekend, although qualifying and race day are expected to be dry. The next race is the Japanese Grand Prix, which will be on 8 October Sunday at Suzuka Circuit.