The German powered to victory in the opening two races of the season in Australia and Bahrain but Hamilton has won in China more times than any other driver, clinching an unprecedented fifth win there past year.
Half a second separates Vettel and Kimi Raikkonen on the front row from Bottas and Hamilton behind them, striking a psychological blow to the Silver Arrows as they bid to kick-start their season.
Hamilton cut a frustrated figure as Ferrari ended Mercedes' six-year grip on Chinese Grand Prix pole in emphatic fashion on Saturday.
Vettel, who put in an error-strewn first attempt, then pulled out just enough through the final corners to deny the 38-year-old what would have been his first pole since last year's Monaco Grand Prix. "The pace just wasn't there".
The Prancing Horse replicated their advantage, with Raikkonen and Vettel setting an impressive pace on the more durable rubber. Max Verstappen was fifth quickest in both sessions, closing in to end the day 0.341 seconds off Hamilton's pace.
Hamilton and Bottas headed back out on another set of soft tyres while Ferrari opted for the ultrasofts.
Lewis Hamilton has admitted "it was a hard day" for his Mercedes AMG Petronas Motorsport team after he qualified fourth for the Chinese Grand Prix.More news: Trump says he backs 'cooperative' approach to Russian Federation probe
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Vettel had the quickest lap in qualifying, posting a time of 1 minute, 31.095 seconds, on the 5.451-kilometer course.
Vettel will, however, go into qualifying later on Saturday as favourite to break the German marque's stranglehold and hand Ferrari only their second pole in China.
On the second runs, Bottas improved but stayed third while Hamilton aborted his lap after a mistake at the hairpin leaving the Ferraris to battle it out for pole.
Hamilton ended the morning session fastest by a comfortable margin.
Carlos Sainz once again left it late for Renault, scraping into Q3 at the expense of F1's Power Rankings leader Kevin Magnussen in the Haas, with the top 10 drivers separated by just one second.
The third row will be made up of the two Red Bull cars. But can they convert a first pole in Shanghai since 2004 into victory?
All the race day attention will be on the famous Italian team though after making a cracking start to the season with wins in Melbourne and Abu Dhabi already and both cars up front in Shanghai.