Scampering ahead of Théo Pourchaire at the start, Lawson spent the majority of the race in a to-and-fro with his former Formula 3 rival, before seeing the ART Grand Prix driver retire.
This handed the Kiwi a more experienced challenger, as Daruvala – up from fifth - lined up behind him. However, the Carlin driver had no answer to his Red Bull academy teammates' defensive masterclass and was forced to settle for second.
In the second race, Lawson was sitting third when he crashed out to miss out on another podium finish.
Reigning Formula 3 champion Oscar Piastri went onto win race two for his maiden F2 victory.
Lawson sits fourth on the standings heading into tomorrow's feature race.