Barnicoat made a good start from Saturday's qualifying position of fifth, to move up a place off the grid when the lights went out.
From there, the top four drivers quickly began to stretch their advantage between themselves, with Barnicoat over a second behind Hitech GP team-mate George Russell after only six laps. The top two drivers, Prema pair Lance Stroll and Nick Cassidy entered into a private scrap of their own.
In the middle part of the race, Barnicoat held off the attentions of Prema's pole-sitter Maximilian Gunther, before sprinting clear of any further attacks from behind. He was unable to challenge Russell for third though, ending the race 1.8 seconds in arrears.
Stroll came out on top of the tussle for race victory, with Russell five seconds behind in third.