Bamber had won a scholarship to enter the championships this year with the Fach Auto Tech team and. in his debut in Barcelona, he beat Austrian Philipp Eng (Team Project 1) and Great Britain's Ben Barker (Verva Lechner Racing Team) to the flag.
Bamber punched the air as he revelled in his maiden Supercup win.
"This is totally unbelievable. How fantastic is it to kick off my first season in this series with a win. I'm quite happy if it continues like this," he said.
Eng took pole position during qualifying on Saturday by the barest fraction, beating Bamber by 18-thousandths of a second.
But on Sunday, Bamber got the jump off the line with his 911 GT3, which is based on the seventh generation of the Porsche 911 and brings 460 horsepower to bear.
Bamber would then hold the Austrian off to win by five seconds.
"Unfortunately, my grid position was completely in the shade and the track was still damp from rain during the night," said Eng.
"The sun had already dried the second spot and for this reason I had no answer to Earl and he was simply faster than me in the race."
Barker got up to third after starting seventh on the grid in the 12-car field.
"During 2013, I didn't manage once to finish in the top three and now I do it at my first race of the season. That was a fantastic moment," he said.
Bamber takes 20 points from Barcelona to lead the series by two points from Eng, while he is well clear in the rookie standings of three drivers with Alex Riberas (McGregor, Attempto Racing) sitting on 12 points.
The next Supercup round is on the famous 3.34km Monte Carlo street circuit on May 22-25.