Maini started from P3 on the grid on prime tyres and held on to his position for several laps while Arthur Leclerc was right behind him putting pressure on the softer tyres.
Leclerc got past Maini but the Indian fought back and made a last second dive onto the inside and got back P3.
Leclerc kept the pressure on through the safety car restarts as well, but Maini held on to a well-deserved maiden podium in F2.
"I have been waiting on the doorstep of getting onto a podium and narrowly missed it at Bahrain," the 22-year-old said.
"It was great to get my first podium on a new track as a rookie. It is most important to keep consistent as it’s a very long series. We have had a good start to the season so far with consistency in qualifying always in the top 8."
Dennis Hauger (MP Motorsport) and Jak Crawford (Hitech Pulse-Eight) took the top-two finishes.
The other Indian in the fray, Jehan Daruvala driving MP Motorsport had a disappointing 17th place finish.