Emotional Button hails strong McLaren start
The celebrated British marque finished the weekend on top of the constructors' standings, with Danish debutant Kevin Magnussen brilliantly placing second and Button third.
The results followed a season without any podium placings at all last year for McLaren, prompting an internal coup with team boss Ron Dennis returning to a more hands-on role.
Both drivers were elevated by one spot after Red Bull's Daniel Ricciardo was disqualified from second place for a technical infringement. Mercedes' Nico Rosberg was the winner.
For Button, it was a triumphant finish to a difficult first grand prix without his father John, who was ever-present at his races but died suddenly in January.
"It's been an emotional day for me, but it's been great to have my sister, my fiancee and lots of friends around me, so that definitely helped," Button said.
In a touching tribute, the 2009 world champion updated his Twitter picture using an old photo of himself as a young child with his father.
Button said: "As a team, I think we can be very proud of the job we did today.
"I don't think we expected to be leading the constructors' world championship at the end of this weekend, but I think the pace in the car is generally there."
Magnussen, 21, admitted it was "surreal" to become the first Danish driver to reach an F1 podium -- and in his very first race in the sport.
"It's just fantastic to be on the podium! What happened today just feels surreal. Being on the podium in the first race of my Formula 1 career -- it's amazing," he said.
McLaren's newly installed racing director Eric Boullier called Magnussen's performance "one of the finest performances by a Formula 1 rookie in living memory.
"Despite his youth and inexperience, he drove like a man who'd notched up 100 grands prix already," Boullier said.
"It was a complex and challenging race, yet he managed those complexities and challenges faultlessly."