Bottas posted the best lap of the weekend to date around the Losail International Circuit with a time of one minute 22.310secs to finish 0.078s clear of team-mate Lewis Hamilton.
For championship leader Max Verstappen, the final hour-long run was plagued by rear-wing issues that required repairs throughout the session.
With only 10 laps to his name, compared to 17 and 16 for Bottas and Hamilton respectively, the Dutch driver was third quickest but 0.341s adrift.
Overall, it was a typical FP3 for a night race - mostly fact-finding given the unrepresentative conditions with qualifying and the grand prix taking place at night under the lights.
In bright but hazy conditions given the light cloud covering, track temperatures only reached a high of just under 37 degrees, playing into Mercedes' hands.
The lead at the top of the timesheet changed hands on numerous hands, Alpine's Esteban Ocon setting the early benchmark before Hamilton ousted the Frenchman, only for Fernando Alonso to go top on medium tyres in his Alpine.
Bottas then posted a 1:23.387s to lead the way but was soon beaten by Hamilton, only for Verstappen's first flying lap to seemingly suggest 'game on' for qualifying with the quickest lap of the weekend to date.
Verstappen had to wait for half an hour before finally emerging from the garage as Red Bull were again forced into rear-wing fixes, a component that has plagued them over the last few races.
At this track, in particular, the DRS actuator - the upper part of the wing - was visibly flapping at high straight-line speeds, and continued to do so in FP3.
Over the next few minutes, though, Mercedes then laid down a marker as Bottas moved four-tenths of a second clear of Verstappen with a 1:22.573s, with Hamilton finishing 0.082s behind the Finn.
That time gap to Verstappen was predominantly as a result of Mercedes being quicker through the medium-speed corners.
On their final flying soft-tyre runs, Hamilton and Bottas again traded times, with the latter having the final say with his 1:23.310s.
With under seven minutes remaining, and following further rear-wing repairs, Verstappen finally appeared again on a new set of softs but off the pace compared to the Mercedes duo.
Towards the end of the session, Red Bull claimed the situation had been improved but had not been totally solved.
AlphaTauri's Pierre Gasly, enjoying another strong weekend, was fourth fastest ahead of Red Bull's Sergio Perez, but with both just over half-a-second adrift.
After missing all of the more relevant FP2 following a chassis change, the Russian driver also sat out all of FP3 bar a few seconds.
Just a minute after the session had started, Mazepin had reached the end of the pit lane when he was ordered to immediately stop the car.
FIA race director Michael Masi was forced to red flag the session for four minutes to allow the car to be retrieved by the Haas mechanics who rolled it back into the garage. It was later discovered the engine control unit needed to be changed.
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