The pair endured a difficult opening day of practice at Barcelona as Mercedes finally got some proper running of its new W14 upgrade package.
The struggles even left Hamilton feeling that he would not make it through to Q3 in qualifying because the car was so difficult to drive.
But a late-night simulator session for Schumacher back at Mercedes' Brackley factory on Friday helped unlock the answer that the squad needed for its set-up and ultimately set the course for its first double podium finish of the season.
Speaking after the race, runner-up Hamilton said that Schumacher had to take the credit for delivering the step forward Mercedes needed after the first day of practice.
"Friday was a real struggle with the balance, it was way out of the window," explained Hamilton. "It was very hard to drive, very unpredictable. And then we did some great work overnight.
"We've got a great team, with Mick back in the simulator on Friday night, and he did some great work, which helped us get on the right track on Saturday."
Russell, who charged from 12th on the grid to finish third, said that from Saturday onwards, the Mercedes had felt the best it had ever been around Barcelona, even though he had some struggles with the handling in qualifying.
"It probably felt the best it's ever felt around Barcelona because of the cooler conditions," he said. "Definitely this season, it is probably the best it's felt, the most together it's felt.
"The team's done a really, really great job. The work that Mick and the simulator team are doing overnight, they were there well past midnight to help us with the set-up and get it in a good window for the race today.
"So, we are making strides in the right direction. We just need to make sure, especially into next year, that we hit the ground running because I think we as a team probably develop faster than anybody else."
With Mercedes having abandoned its zero pod concept, Hamilton felt the car was now better than it had ever been in the current ground effect era.
"It is definitely the best the car's been the past year and a half," he said. "So that's kudos to the amazing group of people we have back at the factory who continue to work hard and push the car forward.
"It felt the best this weekend; it felt the best yesterday [in qualifying] and today [in the race] better than it's felt for the past 14/15 months, whatever it is.
"That's super encouraging, I think not only for me but for everybody in the team. This will be a big boost for everybody's morale. And we're going to take that energy on to developing the car."
Schumacher will get his first run in Mercedes' current F1 car during the post-race tyre test at Barcelona that the team is conducting for Pirelli this week.
