The Aston Martin driver was just 0.005s clear of his Red Bull rival, their times set just seconds apart during the latter minutes of the hour-long encounter.
It's a performance that serves only to build the intrigue heading into qualifying, with Aston Martin and Alonso having impressed many in the paddock since pre-season testing.
Red Bull programme
For 25 minutes the Red Bull duo remain in the garage before finally emerging with a set of hard compound tyres fitted.
They did so as Alonso completed a qualifying simulation, the Aston Martin driver logging a 1:33.121s on a set of the softs.
It saw the Spaniard move 0.374s clear at the top of the timesheets.
Max Verstappen and Sergio Perez weren't drawn into chasing Hollywood lap times at that point, but even still the latter's initial timed lap was within a second of Alonso's suggesting the two-time world champion was not on the ragged edge.
Perez's pace was telling as it came on the slowest compound of tyre – the preferred race tyre after the C2 on Friday proved the weakest of the three available to teams this weekend.
Verstappen also had positive pace on the white-walled rubber as he sat 0.583s away from Alonso's best after his first timed lap.
Hamilton the early pacesetter
Hamilton was the fastest before the true qualifying simulations began, his 1:33.495s the benchmark for the better part of the opening 20 minutes.
His early best saw him half a tenth quicker than next best Carlos Sainz and a tenth up on Charles Leclerc.
All had used the soft rubber for their efforts despite the hotter ambient conditions of final practice versus those that will be seen in qualifying.
Through the middle part of the session, Ferrari was clearly working on long-run performance with both drivers lapping seconds adrift of the outright pace.
Inside the final 20 minutes, Zhou Guanyu signalled the beginning of the true qualifying simulation phase of the session.
The Alfa Romeo Sauber driver managed a 1:33.180s to rise to second fastest, only for that to quickly become third when Lance Stroll went quickest.
Stroll logged a 1:32.919s to depose his team-mate from the top of the timesheets, 0.202s quicker than Alonso to make for an Aston Martin one-two with 15 minutes remaining.
Next was the turn of Hamilton, who was 0.2s faster than Stroll to the first split, doubling that advantage at the second.
He crossed the line with a 1:32.555s, the fastest time to that point, and a 0.176s improvement on George Russell who'd flashed across the line seconds prior.
As the Mercedes duo completed their laps, Verstappen was on a preparation lap, starting his qualifying simulation with 10 minutes to run.
It was a solid if unspectacular opening sector, 0.02s slower than his 2021 title rival.
However, he found time through the middle part of the lap, ending it with a 1:32.345s to shoot – very temporarily – fastest.
That's because almost in his wheel tracks was Alonso, who went 0.005s faster to claim top spot by 0.005s.
Perez was a tenth back from his team-mate when he finally completed his timed lap, five minutes prior to the chequered flag.
As the final hit out prior to qualifying, the session reaffirmed much of what has been suspected – though stopped short of confirming the true pecking order.
Aston Martin's pace looks genuine, though what Red Bull is holding back, if anything, is unclear.
Mercedes looks half a step off the pace, with Ferrari seemingly trailing in their wake. Beyond that, the midfield pack remains as tightly woven as ever.
Oscar Piastri was seventh best following his qualifying simulation, dropping to ninth at the chequered flag, though whether that's genuine – and it is thought McLaren will struggle in the early race – remains to be seen.
Regardless, his 1:33.045s was a promising time given he banked just 11 laps in the sesion, leaving him the better part of 0.2s faster than team-mate Lando Norris.
Practice in Bahrain is now complete, with qualifying next for teams at 18:00 local time (02:00 AEDT).
Results: Bahrain Grand Prix, Free Practice 3
|Alfa Romeo Sauber
|Alfa Romeo Sauber
|Nyck de Vries