The winner of the Bahrain Grand Prix a week ago, Verstappen headlined FP1 in Jeddah with a 1m29.659s on the soft compound tyres, taking the top spot from Mercedes' George Russell in the process.
His time looked ominous, although Alonso got to within 0.2s of the Dutchman's time to split the two Red Bulls at the top of the timing order in the daylight session - like last weekend, in conditions not entirely representative of those set to be experienced in the night-time qualifying and race.
Breezy conditions at the Jeddah Corniche Circuit, with a 20km/h headwind along the main straight according to Carlos Sainz's radio traffic, ensured that the back end of the circuit added further challenge to the sweeping corners in the second and third sectors.
In their exploratory laps around the circuit, the field was split between the medium and hard tyres; Pirelli had selected C3 and C2 respectively for this weekend to mirror last year's tyre allocations.
Russell posted the best lap in the opening half-hour, going top with a 1m30.806s before whittling it down to a 1m30.554s to throw down a benchmark.
Lando Norris then put together the first competitive time on soft tyres after the halfway point, setting a 1m30.424s, which was beaten by Max Verstappen's 1m30.014s on the Red Bull driver's first effort on the red-walled C4 rubber.
By a scant 0.003s, Russell reclaimed his position at the top of the timing board and sat there for about five minutes, before Verstappen once again laid down the gauntlet with the first time below the 90-second mark - which ultimately proved to be the fastest lap of the session.
Russell managed to draw closer with a 1m29.939s on his next lap in an attempt to fortify the runner-up spot, but Perez's 1m29.868s proved enough to move up to second.
Alonso, who had looked competitive in the earlier hard-tyre running, posted a 1m29.845s to beat Perez - whom he diced with for the lead in the early stages of last year's race.
Having dropped behind Alonso and Perez, Russell had to be content with fourth in the overall times, narrowly beating the Ferrari duo of Charles Leclerc and Sainz as the Ferrari drivers completed the top six.
Norris was seventh overall, just over half a second shy of Verstappen's time, and only 0.005s clear of Lewis Hamilton. The Mercedes driver had earlier complained of bouncing on the rear of his W15, and asked the team to promptly find a fix.
There was a near 0.4s gap between he and Lance Stroll, as the Canadian recovered from an early scrape with the Turn 21 inside wall to set the ninth-fastest time. Stroll had clipped the barrier with his front-left wheel and had to retreat to the pits, as his wheel cover had made a break for freedom following the impact.
Alex Albon completed the top 10 as the Williams driver found strong pace on the medium tyre, but was a second shy of the best lap set by ex-team-mate Verstappen and a handful of hundredths clear of Valtteri Bottas' Sauber.
Daniel Ricciardo was 12th fastest, although did his best lap on a set of mediums to sit ahead of Alpine's Esteban Ocon and Williams' Logan Sargeant.
