The Racing Steps Foundation-backed driver, who also scored a top-10 finish in the previous day’s second race of the weekend, headed into the finale from 12th place on the grid with a fresh set of two tyres to aid his progression.
With the race eventually getting underway following a two-hour postponement due to severe foggy weather, Barnicoat made an excellent getaway.
The Hitech GP racer made up four places on the opening lap to move up to eighth place, but on lap two, was forced to take a wider line into the hairpin to avoid his team-mate Nikita Mazepin.
The Russian had taken too much speed into the tight right-hand turn, and locked up his right front wheel.
In his avoidance of the incident, Barnicoat ran over the outside kerbs, tagging the Mucke Motorsport machine of David Beckmann in the process, with the German picking up a race-ending puncture.
The incident demoted Barnicoat two places in the order as both Mazepin and fellow team-mate George Russell went by.
But Russell’s day would soon end as he retired in the pit lane, and Barnicoat soon re-passed Mazepin towards the end of lap 13, before quickly charging past the Prema machine of Ralf Aron into seventh place.
Ahead, Motopark’s Sergio Sette Camara ran 1.5 seconds ahead, but Barnicoat who had struggled with a significant lack of straight-line speed throughout the weekend, reduced the Brazilian’s advantage to only 0.6 seconds by the time the chequered flag signalled the end of the race, and the end of the season.
Barnicoat finishes the season ninth in the overall drivers’ standings. Having led the Rookie class points in the opening half of the season, a second half of struggles results in a fourth place finish.
Championship winner Lance Stroll wrapped up his third race victory of the weekend, ahead of Motopark’s Joel Eriksson who also won the championship’s Rookie class title. Carlin’s Jake Hughes took third place.