The German, two points behind Renault's Alonso with three races to go, was fifth fastest on a grey and gusty Shanghai afternoon with the Spaniard sixth.
The two had kept out of each other's way in the morning, with Alonso watching and waiting from the pit wall as a string of test drivers kicked off what promises to be a crucial weekend for both men.
Austrian reserve driver Alexander Wurz was quickest for Williams in both sessions, with a lap of one minute 35.574 seconds in the morning and 1:35.539 in the afternoon as the weather deteriorated into a steady drizzle.
German teenager Sebastian Vettel, who has set an impressive pace in his two previous Friday appearances for BMW Sauber, was second on the afternoon timesheets. Neither he nor Wurz will race on Sunday.
Seven times champion Schumacher was fourth in the morning after completing a mere four laps beneath the towering but near-empty
The German has 90 wins to his credit but is yet to register a point from two appearances in Shanghai.
Alonso, winner in China last year on his way to becoming Formula One's youngest champion, habitually sits out the opening practice session to limit the mileage on an engine that must last for two races.
He has a new and more powerful unit in China after a failure at Monza three weeks ago.
"I am very confident, as always," the Spaniard had told reporters on Thursday.
"I think that for the last three races we should be very competitive... the car is really at maximum performance now, with no problems.
"We should be very quick. Now it is up to us and Ferrari to decide who is quickest," he added."
