Vettel topped the timesheets despite suffering from reliability problems during P2 as at one stage an electrical problem caused a complete shutdown of his auto.
Bottas was just 0.041s off Vettel - losing most of his time to the Ferrari in the middle sector - while Ricciardo was just another 0.025s off in third.
Ricciardo finished third in the day's second practice session, followed by Ferrari's Kimi Raikkonen.
But early on in what was expected to be a long run to evaluate race performance, Vettel's auto suffered what he called a "complete shutdown" over the radio.
"Complete shutdown", he told his team as he nursed his auto back to the pits.
Even Lewis Hamilton is relishing the battle - "I love this fight that we are having", the Briton said after embracing Vettel in parc ferme last weekend. The vehicle feels good. "On one lap it was OK", Vettel said. Raikkonen was hit by engine trouble during the first practice session, Vettel's vehicle slowed to a complete stop with about 40 minutes left in the second session due to a "complete shutdown". The Finn needed a new internal combustion engine to be fitted as well ahead of the second session. As a result, Mercedes focused on wider development during the 90 minute session and did not set representative lap times on the soft tyres.
He aborted his first attempt and backed off after a big oversteer moment in Turn 1, and on his second try he ran off the track at Turn 10 after locking up trying to get around Nico Hulkenberg's Renault.
The two drivers have one win each so far this season from the first two races, in Australia and China, and look likely to be vying for the title over the next eight months.
"It was incredibly hot early on, with some of the very toughest conditions, both physically and in terms of working with the tires", Hamilton said. The race is a 191-mile contest that will run 57 laps around the track.
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Yes, we have a tough run in but it is still close". "He is very good to play for the team". But make no mistake: this game will mean everything to the Portuguese.
Ferrari was quick despite problems.
"We were lucky to recover to get some laps in the end".
"I honestly think our relationship will stay the way it is", Hamilton told The Guardian.
Red Bull team boss Christian Horner told BBC Sport the team had made some changes to the vehicle and it had been "a positive day", especially for Ricciardo.
"Obviously we were quite busy and had a bit of an issue".
Verstappen ended up eighth overall, almost a second off the pace and behind both Hulkenberg and Felipe Massa in a competitive session.
The Dane, Esteban Ocon, Jolyon Palmer and Fernando Alonso were split by just four hundredths of a second.
Ricciardo and teammate Max Verstappen slotted into second and third respectively shortly after Vettel set his time, with nearly half-a-second separating the Red Bull pair.
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