The 41-year-old Spaniard, revelling in the performance of his vastly-improved Aston Martin car, clocked a best lap of 1 minute 32.340 seconds to edge Red Bull's two-time defending world champion by 0.005 seconds.
The Dutchman's Red Bull team-mate Sergio Perez was third ahead of seven-time champion Lewis Hamilton of Mercedes, Charles Leclerc of Ferrari and George Russell in the second Mercedes.
Lance Stroll, looking recovered from his wrist injuries after a pre-season cycling accident, was seventh in the second Aston Martin, ahead of Carlos Sainz in the second Ferrari and rookie Oscar Piastri of McLaren, who was not born when Alonso made his F1 debut in Melbourne 22 years ago.
Pierre Gasly was 10th for Alpine.
Verstappen and Red Bull appeared unperturbed by this relatively minor setback, but Alonso's continued near-perfect form and calm demeanour suggested the champions may struggle again at one of their least-favourite circuits.
The Dutchman has never won a season opening race or in Bahrain, after nine attempts, while Red Bull have not triumphed at the Bahrain International Circuit for ten years.
On another hot day at Sakhir, with a track temperature of 42 degrees Celsius delivering challenging and unrepresentative conditions, there was no rush out of the pitlane at the start.
When Russell joined the fray after 10 minutes, he was only the fourth man on track, but his arrival sparked others to venture out.
Hamilton soon topped the times ahead of Leclerc as Ferrari and Mercedes duelled for speed.
After delaying his arrival, Alonso made an immediate impact and was top after 55 minutes on softs as Verstappen joined in, going fifth on hard tyres and complaining of lack of grip.
In the extreme conditions, it was little surprise the hard compounds failed to perform as Stroll took over at the top, ahead of his Aston Martin team-mate, with 15 minutes remaining.
Mercedes then switched to softs and Hamilton and Russell took over before Verstappen and then Alonso outpaced them to go first and second.
Told he had taken P1, Alonso gave a laconic reply. "Oh, really?" he drawled.
As a brief rehearsal ahead of qualifying later Saturday, it was intriguing, but confirmed Aston Martin are genuine front-runners for this weekend's event.
