However, Verstappen's near ideal day was soured in the final 30 seconds of the session as he lost the rear of his Red Bull at the apex of Turn 1 and slammed into the barrier.
The session was red-flagged with just under 20 minutes to go, when Sergio Perez crashed heavily at the narrow Turn 8.
The incident followed a prickly interview between Palmer and BBC reporter Jennie Gow on the pre-event media day on Thursday.
Red Bull have a trick up their sleeves?
But the Dutchman's impressive form continued.
Hamilton was fast on the soft compound tyres, but never got decent runs on the supersoft and finished the evening session 10th with the time he set on the former.
The session ended with a Red Bull 1-2 (a while since we've had one of those!), with Vettel, Perez, Hamilton, Bottas, Ocon, Massa, Raikkonen and Kvyat rounding out the top 10. A few cars headed back out, but apart from Grosjean complaining about his brakes again, there was nothing much to phone home about. He complained about his rear being a bit weak, not allowing him to get the power down effectively.
"The only driver who had a clause was Mr Vettel".
Williams rookie Lance Stroll was an impressive sixth quickest, two weeks after scoring his first points at his home race in Canada.
The gloves are off between Hamilton and Vettel
Lewis Hamilton accused Sebastian Vettel of driving dangerously during the Azerbaijan Grand Prix on Sunday. He was obviously sleeping and drove into the back of me.
However, that all changed on the next lap, Hamilton overcoming his problems to go clear by a whopping seven-tenths, nearly a second faster than his time sheet topping FP1 time past year.
"The track is hard. But if we can get a auto on the first couple of rows here, it will be a great result".
It is the fourth retirement Verstappen has suffered in the last six races, and none have been of his making.
Vettel, by contrast, had a solid day.
Mercedes' Valtteri Bottas and Verstappen's teammate Daniel Ricciardo made for top three.
Vettel was quickest, but there was little to choose between him, Bottas and Verstappen.
"Most of the cars had problems today".
"We are again up close to Ferrari, or even [potentially] in front - so that is good", he said.
Starting at the back on Sunday will be the McLarens of Stoffel Vandoorne and ex-champion Fernando Alonso after a latest round of engine problems and according grid penalties.
But he said running the engine on reduced power due to a rev-limiter problem, a lock-up and a subsequent problem with gear-synchronisation all led to him qualifying further back than the vehicle was actually capable of.
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