Ferrari saw its engine performance take a significant hit in 2020, leaving its works squad and the customer outfits, Haas and Alfa Romeo, on the back foot compared to their rivals.
Ferrari made decent progress with its engine last year, and had a late-season boost thanks to an updated hybrid system that was intended for 2022, giving it confidence heading into the new campaign.
Qualifying in Bahrain proved Ferrari's step forward with the power unit as Charles Leclerc took pole, while teammate Carlos Sainz secured third on the grid. Alfa Romeo's Valtteri Bottas will line up sixth ahead of Haas driver Kevin Magnussen in seventh.
It has been suggested that Ferrari's engine power advantage could be worth as much as two tenths of a second per lap over the rest of the field.
The step forward prompted Haas boss Steiner to claim after qualifying that Ferrari now has the best engine in F1.
"I think the Ferrari engine is now the best engine," Steiner said.
"I honestly think that, and that gives a lot of credit to them because they were in the same position as us. They had to take a lot of s**t from people about it.
"And they just got back, did their homework and came back with something very good."
Bottas will line up on the third row for his first race with Alfa Romeo, and felt there were no longer "any more big differences between any of the engine manufacturers".
"I think Ferrari has done a good job, they've definitely made a step forward from last year," Bottas said. "So that is an improvement, no doubt."
Max Verstappen qualified second on the grid for Red Bull behind the two Ferraris, missing out on pole position by 0.123 seconds. The reigning world champion said that while Ferrari's performance was "not just down to the engine", the team was "clearly going well on the straights".
AlphaTauri's Pierre Gasly managed to reach Q3, but noted "the Ferrari-powered cars are really fast", meaning his team has "got some work to do if we want to get to the top of the midfield".
Q1 saw four Mercedes-powered cars get eliminated along with Yuki Tsunoda, whose AlphaTauri is powered by a Red Bull-badged Honda power unit.
McLaren lost Daniel Ricciardo in the first stage of qualifying, seeing the Australian drop out in 18th, while Lando Norris was eliminated in Q2 after finishing 13th.
When asked about engine parity, McLaren F1 chief Andreas Seidl felt the team had to focus on comparing itself to the works Mercedes outfit which runs the same power units.
"We have to acknowledge independent of these issues we had that we simply didn't have the performance," Seidl said.
"The most important thing is for us now to simply acknowledge that, and compare us to the Mercedes works team. We miss around a second to Mercedes. That's the best reference for us we can have, and that's what we are focusing on as a team.
"We know we most likely simply miss grip, which is probably a result of missing mechanical grip plus aerodynamic grip, and it's simply important now to put all our energy into making sure we find performance as quick as possible."
Additional reporting by Adam Cooper and Ronald Vording.
