Ferrari president Sergio Marchionne said "it was about time" Ferrari returned to winning ways after triumphing in the Australian Grand Prix.
Sebastian Vettel beat Mercedes rival Lewis Hamilton to give Ferrari its first win since the 2015 Singapore Grand Prix after jumping ahead during the pitstops.
The victory also means a non-Mercedes driver leads the championship for the first time since 2013.
Vettel's teammate Kimi Raikkonen finished in fourth to help Ferrari lead the constructors' championship.
"It was about time," said Marchionne in a statement released after the race.
"I am delighted for the team and for our tifosi who stood by us throughout this whole period.
"We've been waiting for this victory for almost a year and a half. Hearing the Italian national anthem again was very moving.
"Sebastian delivered a great race and I am sure Kimi will be soon up there battling alongside his teammate.
"Of course, this victory is something to share with the entire team, both at the circuit and back in Maranello, because teamwork is the only way to achieve major goals."
Marchionne insisted the victory was only the first step in a very long championship and urged his team to remain focused.
"Now, however, it is absolutely essential to remember that this is not the destination but the first step on a long road that must see us all focused on improving each and every day," he said.