The championship leader, a point clear of Mercedes team mate Lewis Hamilton after two races, set a benchmark time of one minute 33.330 seconds in the afternoon.
The Finn was just 0.027 seconds clear of Vettel, who was fastest in the morning by a 0.207-second margin ahead of Hamilton.
"We made it to the top of the timesheets but it is always very difficult to find a good balance through an entire lap on this track," said Bottas.
"Ferrari still seem to be quicker than us on the straights, whereas we were better in most corners in FP2 (the second session)."
Red Bull's Max Verstappen was third fastest in the afternoon, 0.221 seconds off Bottas’ best, but the 21-year-old struggled with shifting gears and clutch issues throughout the session.
His Honda-powered team won in China last year, when they used Renault engines, with Australian Daniel Ricciardo.
Hamilton, the most successful driver by far around the 5.4-km Shanghai International Circuit with five wins to date, ended the day fourth.
DIFFICULT DAY
Ferrari arrived in China as favourites after looking dominant in Bahrain, a race they would have won but for a late engine problem that hit Charles Leclerc's car while leading, and with plenty of straight line speed.
Vettel led the opening session, and was hot on Bottas’ heels in the afternoon, while Leclerc had a difficult day.
Both the 21-year-old Monegasque and Vettel are running a new electronic control package as a precaution against a repeat of Leclerc's engine problem.
The youngster's session ended early as he parked up in the garage with some 20 minutes to go so that Ferrari could carry out cooling checks.
"We had to stop for further checks on something on the oil," said Leclerc. "We will check it but no big issues.
"I think it will be very close, Mercedes and also Red Bull are actually quite close, so it will be an interesting battle."
Hamilton was second fastest in the morning but struggled in the afternoon.
"We’re going to work hard tonight to find some tweaks and hopefully come back stronger tomorrow,” said the five-times champion. "The car has the pace in it to compete at the front, we just need to find the right set-up."
Nico Hulkenberg was fifth fastest for Renault, ahead of Carlos Sainz in the McLaren.
McLaren rookie Lando Norris, fresh from having scored his first Formula One points in Bahrain, was eighth for McLaren ahead of Renault’s Ricciardo.
Red Bull’s Pierre Gasly rounded out the top 10.
Friday’s two sessions were relatively trouble free apart from a few spins as the drivers explored the limits and got to grips with the track.
Hamilton and Bottas both spun during the second 90 minutes while Canadian Lance Stroll lost control of his Racing Point at the exit of the final corner in the morning.
The brakes on Alex Albon’s Toro Rosso also caught fire at the end of the session with Ferrari mechanics standing close by and helping to douse it.
(Reporting by Abhishek Takle in Shanghai; editing by Greg Stutchbury/Amlan Chakraborty/Alan Baldwin/Pritha Sarkar)
