Verstappen's puncture came as a result of contact with Hamilton, as the Dutchman had just made a move down the inside of the Mercedes at Turn 1 but then his left rear came into contact with Hamilton's front right.
By lap eight of 57, Hamilton was up to fourth and homing in on a podium place.
"The auto felt okay, but we need to find some more pace especially on a single lap".
Although it is very early, Mercedes is not looking the unshakeable, supremely reliable force it was when winning the drivers' and constructors' double in the past four seasons.
"If one guy is getting injured, it is bad for us", he said, after briefly delaying his mandatory television interviews to ask the team about Cigorini's condition, for which he had to ask for permission from a representative of F1 management.
Francesco Cigorini suffered a double leg break. Sky Sports screenshot
"We've been trying to get ahead of the Ferraris, but it has been tough, they just had the pace all weekend".
Raikkonen and Vettel finished half-a-second clear of their Mercedes rivals in practice, and Vettel, while pleased with his team's progress, expressed caution over Friday's times. "But it wasn't quite enough", Bottas said. "The vehicle has been excellent". Valtteri Bottas (Mercedes) +0.699 3. But that came courtesy the timely deployment of the virtual safety auto with Hamilton, until then, set to wrap up a comfortable victory in his Mercedes which had a clear edge over Vettel's Ferrari all weekend.
"Overall, we are a bit happier this weekend". Gearboxes must last for six successive races according to the rules.
Vettel duly retained position across the rest of the lap to record victory by 0.699s, marking the first time since 2004 that Ferrari has started the year with successive wins.
Red Bull's Daniel Ricciardo was fastest in the opening running here in the desert, but the Australian had to make do with sixth under the lights of the Sakhir circuit in the second session. We are happy with how the auto was responding, how the front end was responding - you can also see it in the result. It has been a poor start to the season from him. He span his vehicle after pushing too hard early on in Melbourne two weeks ago and finished sixth.
New Zealand driver Brendon Hartley complained about damage to his left front wing and soon found out why: He hit a bird.