The Mercedes driver's time was a tenth of a second faster in the afternoon practice than McLaren's Lewis Hamilton, who took back-to-back poles to start the season at the Australian GP and Malaysian GP.
Red Bull teammates Sebastian Vettel and Mark Webber had the third- and fourth-fastest times of the session.
Schumacher, a seven-time world champion, has yet to finish on the podium since coming out of retirement in 2010, but this year seems to have a car fast enough to challenge the top drivers.
He was third fastest in qualifying at the Malaysian GP last month — his best qualifying performance since the 2006 Japanese Grand Prix.
"The car handled definitely much better than what we experienced the last three years here," he said after Friday's practice. "We're not yet there where we want to be, but we had a good race." Mercedes' new rear wing design has been a source of contention among rival teams this season. Lotus filed a protest on Thursday arguing that the design broke the rules, but it was rejected by race stewards.
Red Bull has also questioned the wing design, despite it being deemed legal by Formula One officials.
The Mercedes design feeds off the Drag Reduction System — an initiative introduced to Formula One in 2011, which allows drivers to open the rear wing to reduce drag and increase straight-line speed. When the Mercedes' rear wing is opened, it exposes a duct which directs airflow back under the car to increase downforce.
At the heart of the argument is whether the system breaches rules which prevent ducts being operated by the driver. Mercedes says the driver operates the DRS and the ducts are only incidentally exposed.
Schumacher said after the practice session he believes the controversy has been overblown.
"It is a good innovation and I think it should be honored by everybody," he said. "Although it gets overestimated the worth of it, but it's good." Schumacher's teammate, Nico Rosberg, was fifth fastest in the afternoon session, followed by McLaren's Jenson Button, Sauber's Kamui Kobayasi, Force India's Paul di Resta and Nico Hulkenberg, and Ferrari's Fernando Alonso.
The times were considerably faster in the afternoon compared to the morning practice, when a light mist created slippery conditions and most of the top teams stayed off the track until the final minutes.
Hamilton led the morning session, though his top time was about a second slower than his fastest lap in the afternoon. Rosberg and Schumacher had the second- and third-fastest times in the morning.
Hamilton can start no better than sixth in Sunday's race after receiving a five-place grid penalty for changing his gearbox. Still, he believes he has a chance to finish top of the podium after two third-places finishes this year.
"If I can try and qualify as high up as possible then we can still be in for a good race," he said.
While McLaren and Mercedes looked set to duel for the pole Saturday after posting the best practice times, Red Bull believes it will also be in contention after making adjustments to its car following a disappointing Malaysian GP, where Vettel, the defending world champion, finished out of the points.
"If you look at the car, you can see a big difference compared to the set up we used for Malaysia, but driving it's hard to say, as I don't have a comparison to this track," he said.
"It's cooler here than at the last two races; I felt more comfortable, but we'll see. It's tricky to say if we look competitive. McLaren look good in all conditions." Ferrari had another disappointing day in an up-and-down season. Alonso, coming off a surprise win at Sepang, was only 10th-fastest in the afternoon, while teammate Felipe Massa could manage no better than 12th in the morning run.
"You definitely couldn't define today as being fantastic," said Massa, whose struggles this season have prompted speculation that Ferrari will replace him.
The only major incident in the race occurred when Marussia driver Timo Glock locked up while braking for Turn 1, skidded across a patch of gravel and slammed into a wall. He wasn't injured, but he didn't return to the track.
