Hamilton and team-mate George Russell were resigned to finishing fifth and sixth, powerless to keep up with the faster cars from Ferrari and Red Bull under the Sakhir floodlights.
But following a late safety car for Pierre Gasly's blazing AlphaTauri, a dramatic double retirement for Max Verstappen and Sergio Perez in the closing stages meant Hamilton inherited third behind Charles Leclerc and Carlos Sainz, who clinched a 1-2 finish for Ferrari.
With Russell following Hamilton home in fourth, making good early progress through the pack after qualifying a lowly ninth, that meant Mercedes successfully completed its damage limitation quest while it is yet to get on top of its handling issues.
Hamilton said his third place finish was "the best result we could have gotten", with Mercedes' pre-season porpoising struggles continuing in Bahrain.
"Firstly, a big, big congratulations to Ferrari, so happy to see them do well again, that's such a historic, epic team," Hamilton said in parc ferme.
"It's great to see Carlos and Charles up there as well, so congratulations to them.
"It was such a difficult race, we struggled throughout practice. This is really the best result we could have gotten.
"Of course, it's unfortunate for the other two drivers but we did the best we could and I'm grateful for these points."
When asked if Mercedes has upgrades in the pipeline that will start allowing the Brackley outfit to compete with Ferrari and Red Bull on pace, Hamilton acknowledged there "won't be a quick turnaround" to get the most out of the Mercedes W13 car.
"I'm hoping," added the seven-time world champion.
"I'm know the guys are working really hard back at the factory and it is not going to be a quick turnaround.
"I do feel like we've been the best unified team for so long. I know that we all know that... just keep your head down, keep working.
"There's a long, long way to go."
