The defending double world champion, shaking off the stomach upset that had delayed his arrival in Jeddah by 24 hours, clocked a best lap in one minute 29.603 seconds to outpace two-time champion Alonso’s Aston Martin by 0.208 seconds.
Sergio Perez was third in the second Red Bull ahead of Esteban Ocon of Alpine, George Russell of Mercedes and Pierre Gasly in the second Alpine.
"I think we had a positive day, but I think there’s still quite a few things we can improve," reported Verstappen.
"It’s just fine-tuning, with the downshifts. Things we do all the time," he added.
Perez revealed he had suffered mechanical issues.
"Hopefully, we can sort it out for tomorrow," he said.
"And it will bring us more pace so I can have a better idea of where this car is. Today it was inconsistent, difficult to get a proper read.
“We seem to be strong, but the competition is there as expected."
Alonso’s Aston Martin team-mate Lance Stroll was seventh ahead of Nico Hulkenberg of Haas and the two Ferraris of Charles Leclerc and Carlos Sainz, both of whom were equipped with new power units.
Leclerc already has a 10-place grid penalty for Sunday’s race for taking a third electronic control unit of the season.
Seven-time champion Lewis Hamilton was 11th for Mercedes, with a best lap of 1:30.599, a second slower than Verstappen, on the day he announced he was no longer working with his long-serving performance coach Angela Cullen.
Alonso's performance confirmed his speed this year after a strong showing to finish third in the season-opening race in Bahrain, but it was Verstappen who set the pace with some ease.
After Verstappen’s early supremacy in a Red Bull one-two in opening practice the second session began in cooler conditions, the air temperature descending to 25 degrees and the track from 44 to 31.
Stroll was the first man out, Sainz the early pace-setter, but only for five minutes before the world champion once again went top only for Alonso to reply, two-tenths faster.
Stirred again, both medium-clad Red Bulls responded. Verstappen with 1:29.952 ahead of Perez until Alonso, on softs, split them again. His Aston Martin appeared to be the only car capable of fighting with them.
And then Perez clocked a 1:29.902 as last year's pole sitter Leclerc emerged unscathed from a close brush with Nico Hulkenberg’s Haas.
The close dicing at the front continued with the Red Bulls narrowly ahead of Alonso and then a gap of two-tenths to the pack led, after half an hour, by Hulkenberg and Gasly.
The top three were separated by 0.012 before Verstappen, again, lifted the bar in 1:29.603 after switching to softs for a brief simulation of what may lie ahead in Saturday’s qualifying session.
At this time, Russell climbed to fourth for Mercedes, but Hamilton was 11th.
"We need to make some big changes," said Russell in a stern voice. "Yes, copy," retorted his pit wall, seemingly sensitive to the team’s need for a changed approach as they seek to reverse their slump.
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