The sweltering afternoon conditions in Sakhir were not particularly inviting for fast times, with early laps over two seconds slower than during Friday night's FP2.
After some unrepresentative efforts Ferrari's Charles Leclerc went top with a 1m33.574s on softs, a time which was gradually improved upon by first Lewis Hamilton and then Alonso.
The Spaniard, who had caused a stir by topping FP2, led at the halfway mark with a 1m33.121s, ahead of Hamilton, Carlos Sainz and Leclerc.
Verstappen was fifth at that stage, but ominously less than six tenths behind Alonso on the slower hard compound, even as he complained of having "no grip".
The pace picked up after the typical mid-session pause, with Alfa Romeo's Zhou Guanyu briefly appearing in second.
It was the prelude to a flurry of faster times, led by Aston Martin's Lance Stroll. While recovering from a broken right wrist, the Canadian went top with a 1m32.010s with 15 minutes to go, establishing an Aston 1-2.
Mercedes pair Hamilton and George Russell was next up, Hamilton clocking a 1m32.555s to take over the lead, with Russell under two tenths in arrears in second.
Their time in the sun didn't last for long, as Verstappen returned on the soft tyres to take the lead, only for Alonso to beat him by 0.005s with his 1m32.450s.
Alonso's time held until the finish, setting up a tantalising battle in qualifying between incumbent Verstappen and challenger Alonso.
Perez took third one tenth behind Alonso and Verstappen, after initially joining his team-mate on a hard-tyre run.
A late attempt propelled Leclerc to fifth to split Hamilton and Russell, demoting Stroll to seventh.
Sainz also left it late to take eighth, followed by McLaren rookie Oscar Piastri, who showed early promise for the Woking team seven tenths behind Alonso.
Pierre Gasly was the first of the Alpines in 11th, ahead of team-mate Esteban Ocon, Zhou and McLaren's Lando Norris.
Haas duo Kevin Magnussen and Nico Hulkenberg finished 14th and 15th respectively after a low-key start to the session.
As predicted, Williams and AlphaTauri face a battle to stay off the last row. AlphaTauri's Yuki Tsunoda was 16th, followed by Alfa Romeo's Valtteri Bottas, who didn't get a representative lap in.
Williams rookie Logan Sargeant was 18th ahead of team-mate Alex Albon, with AlphaTauri newcomer Nyck de Vries propping up the timesheets.
Qualifying for F1 2023's curtain raiser follows at 6pm local time (3pm GMT) in cooler evening conditions.
F1 Bahrain GP - FP3 results
| Cla | Driver | Chassis | Engine | Laps | Time | Gap | |
|---|---|---|---|---|---|---|---|
| 1 |  Fernando Alonso |
 |
Aston Martin | Mercedes | 13 | 1'32.340 | |
| 2 |  Max Verstappen |
 |
Red Bull | Red Bull | 13 | 1'32.345 | 0.005 |
| 3 |  Sergio Perez |
 |
Red Bull | Red Bull | 12 | 1'32.446 | 0.106 |
| 4 |  Lewis Hamilton |
 |
Mercedes | Mercedes | 17 | 1'32.555 | 0.215 |
| 5 |  Charles Leclerc |
 |
Ferrari | Ferrari | 21 | 1'32.624 | 0.284 |
| 6 | George Russell |
 |
Mercedes | Mercedes | 17 | 1'32.731 | 0.391 |
| 7 |  Lance Stroll |
 |
Aston Martin | Mercedes | 16 | 1'32.919 | 0.579 |
| 8 | Carlos Sainz |
 |
Ferrari | Ferrari | 21 | 1'32.945 | 0.605 |
| 9 |  Oscar Piastri |
 |
McLaren | Mercedes | 12 | 1'33.045 | 0.705 |
| 10 |  Pierre Gasly |
 |
Alpine | Renault | 13 | 1'33.064 | 0.724 |
| 11 | Esteban Ocon |
|
Alpine | Renault | 16 | 1'33.116 | 0.776 |
| 12 |  Zhou Guanyu |
 |
Alfa Romeo | Ferrari | 13 | 1'33.180 | 0.840 |
| 13 | Lando Norris |
 |
McLaren | Mercedes | 16 | 1'33.202 | 0.862 |
| 14 |  Kevin Magnussen |
 |
Haas | Ferrari | 21 | 1'33.381 | 1.041 |
| 15 |  Nico Hulkenberg |
|
Haas | Ferrari | 23 | 1'33.423 | 1.083 |
| 16 |  Yuki Tsunoda |
 |
AlphaTauri | Red Bull | 15 | 1'33.475 | 1.135 |
| 17 |  Valtteri Bottas |
|
Alfa Romeo | Ferrari | 14 | 1'33.629 | 1.289 |
| 18 |  Logan Sargeant |
 |
Williams | Mercedes | 15 | 1'33.665 | 1.325 |
| 19 |  Alex Albon |
 |
Williams | Mercedes | 15 | 1'33.882 | 1.542 |
| 20 | Nyck de Vries |
 |
AlphaTauri | Red Bull | 18 | 1'34.082 | 1.742 |
| View full results | |||||||
