For both drivers, Slovakia saw their first wins of the season, with Tarquini giving the new SEAT 1.6 turbocharged petrol engine its maiden victory.
Chevrolet enjoyed a one-two finish in Race 2 as Rob Huff took his much awaited first win of the season ahead of Yvan Muller.
Huff has now closed the gap to Muller to 27 points, with Alain Menu dropping to third place in the Drivers' Championship table, just a point behind Huff.
Slovak fans came en masse to the first WTCC event in Bratislava with a capacity 25,000 fans enjoying the sunny day and incident-packed racing.
The Chevrolet team leaves Bratislava with a consolidated lead in both the Drivers' and Manufacturers' championships.
