TDS Racing’s Schothorst had won all six of the previous races, but was even pipped for second spot by Costa’s Oregon Team team-mate Fabien Thuner in Germany.
“I joined this competition from the Formula Renault 3.5 Series, so everyone thought I was going to stroll to the title,” Costa said. “But it’s not like that.
“I’ve had to get to know the car and spend lots of time working with Oregon Team, as this is a really competitive discipline.
“It all paid off today with my first saloon-car victory. It puts me back on track and gives fresh motivation to everyone around me. We had to win.”
Costa claimed pole position for both of the weekend’s races ahead of Thuner. Schothorst tried to surprise them at the start, but was overly enthusiastic on his approach to turn one and ran wide.
Kevin Gilardoni (Oregon Team) and Tom Coronel (TDS Racing) followed the front three, while Niccoli Nalio - who started the race in eighth - quickly caught up with the front five.
On the third lap, the Italian began to push in a bid to snatch fifth place from Coronel, but he had to wait until the fifth lap to find the opening. Costa, meanwhile, was opening up a strong lead over Thuner and Bas Schothorst.
Nalio was the first of the frontrunners to make the obligatory trip to the pits, with Coronel forced to retire after coming into contact with the car of Kelvin Snoeks (TDS Racing).
With all the pitstops complete, Costa retained control of the race with slim one-second advantage over Thuner. Schothorst, meanwhile, trailed more than 12 seconds behind Thuner in third.
The tussle between the Oregon Team pair was the main attraction towards the end of the race. Thuner did not force the issue, however, allowing Costa to cruise home to his first victory in the Eurocup Megane Trophy.
Thuner finished second to secure a first one-two of the season for Oregon Team. Despite finishing third, Schothorst maintains a commanding lead at the top of overall standings.
Thuner said: “The season did not get off to the ideal start, but we’ve been working together non-stop to improve the car and many other things. Everything is working well now, and this podium finish is the first step.
“I now hope I can quickly get a victory and fight for the title myself.”
Schothorst added: “Today I made a mistake I’d never made before when I hit the wall on the entrance to the pits. My race should have been over at that point!
“I carried on with a crooked steering wheel and gears that wouldn’t change properly, but fortunately I managed to reach the finish and get the points for third place. It could have been worse.”