Renault's Jolyon Palmer crashed at Turn Eight causing a stoppage for 15 minutes while the vehicle was cleared.
The Renault driver said braking distances had been hard to judge during practice, and that he was caught out by testing their limits.
With 30 seconds remaining, Verstappen lost control of the rear of his vehicle and slid into the barriers. "It's just a case of getting our heads together tonight to work out exactly how to extract that pace".
Valtteri Bottas: "Practice one was quite tricky: we were struggling with the setup of the auto and it wasn't so well balanced".
"So yeah, they have found good set-up for now and we still have work to do on that".
Hamilton, who trails title leader Sebastian Vettel by 12 points ahead of the eighth round of the championship here in Azerbaijan's capital city of Baku, was fifth in the opening session.
Hamilton, a victor last time out in Canada, failed to set a time on the super-soft tyre, the quickest of the three Pirelli compounds available here, after falling foul to Sergio Perez's crash and then traffic.
Alonso is already facing a 15-place grid penalty as a result of a new turbocharger and MGU-H in his McLaren, the sixth of each component.
Vettel, twice, and Williams driver Felipe Massa had near misses on the same turn, while Ricciardo was instructed on team radio to take precautionary measures and go very wide heading into Turn 8 to give himself room.
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Ricciardo is wary that Mercedes and Ferrari will likely improve, but expects it to be a close session. But even he had his moments, nosing towards a wall in Turn 2 soon after going fastest, and then ending his day crashing in to the wall in Turn 1.
The first practice got underway under a clear sky with track temperatures at a blistering 54 degrees C (129 degrees F).
His subsequent lap time gains put him in the 1m43s margin and he ended his first run with a best lap of 1m43.894s.
The Force India driver was one of the more impressive drivers in Baku a year ago, and had been flying through the city circuit before his collision late on.
A disjointed first session had to be stopped for 10 minutes after Force India's Sergio Perez misjudged the tight section at Turns 8 and 9, where he bounced over the entry kerb and smashed into the wall on exit.
The session was restarted after 10 minutes of clean-up, but while many drivers carried on with super-soft runs, Verstappen's lap would remain unmatched.
Haas driver Romain Grosjean endured a particularly troubled time.