Perez held off Red Bull's Daniel Ricciardo to secure third, and with it Force India's first podium since their breakthrough rostrum at Spa in 2009. The Mexican's team mate Nico Hulkenberg finished fifth, helping the team jump up to second in the constructors' championship behind Mercedes.
Rather than being an isolated triumph, Mallya believes the performance reflects the dedication and cohesion of his team, and is confident Bahrain can therefore set the tone for the rest of the year.
"We've shown in the first few races that we have produced a competitive car," Mallya said. "Bahrain was not just a one-off and we've been improving with each race.
"I was very pleased to finally achieve that elusive podium. We've been close a few times in the last few years, but everything came together perfectly in Bahrain. I think it's a reflection of the talent and the passion of this team, and the fact that we have excellent teamwork. There's a great amount of dedication in all areas of the company and a single purpose in mind for everyone.
"We're second in the constructors' championship, which feels pretty special. I know we've only had three races, but nevertheless it's good to be up there. Forty four points out of three races: it's the dream start we were hoping for. But we won't sit back; we are always trying to improve."
Mallya also praised Hulkenberg's role in helping to protect Perez's podium, adding: "In the final part of the race we saw great teamwork as Nico held back the charging Red Bulls who had the advantage of soft tyres. Ricciardo did eventually get ahead, but Nico helped Checo escape up the road and build a gap. So I was very proud of my drivers; they were outstanding in the race."