Force India's Sergio Perez had a sizeable accident after misjudging the tight section in the old town of Baku.
The Mexican bounced over the entry kerb and smashed into the wall on exit.
The impact, at Turns Eight and Nine, where the track heads uphill towards the medieval castle, tore off both right-hand wheels, the rear one becoming completely detached from the car, and sprayed the track with carbon-fibre debris.
The session was stopped for 10 minutes while the mess was cleared and the car removed from the track.
When it resumed, there was only six minutes remaining, and with a lap that is nearly two minutes long, there was only time for a maximum of two further laps, and there were no further improvements.
Vettel's lap time on softs effectively made him the de facto quickest in the session but the Red Bulls were surprisingly quick on a power track where they are not expecting to do well.
Hamilton also set his best time on the soft tyre and was just over half a second slower than Vettel.
Team-mate Valtteri Bottas did manage a quick lap on the super-softs but was 0.240secs slower than Hamilton's best time on softs.
The initial auguries are not that encouraging for Mercedes, who struggled in Russia in April on a track with many similarities to the Baku street circuit, but the session was not conclusive enough to be certain of what the times meant.
Perez ended the session fourth quickest, with team-mate Esteban Ocon seventh, and Williams' Felipe Massa in eighth ahead of Ferrari's Kimi Raikkonen and Toro Rosso's Daniil Kvyat.
A number of drivers struggled with locking wheels into the tight right-angled corners that abound in Baku, including Renault's under-pressure Jolyon Palmer.
The Englishman twice ran wide at Turn One at the end of Baku's super-long straight and ended up only 18th fastest, 1.3secs slower than team-mate Nico Hulkenberg.
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