Barnes gets $4.5 million, Brasier $1.25 million, Brice $870,000 and Plawecki $1.6 million.
A day earlier, the Red Sox agreed to an $8.3 million, one-year deal with left-hander Eduardo Rodriguez.
Third baseman Rafael Devers is Boston's only remaining player eligible for arbitration.
Barnes took over as Boston's closer after Brandon Workman was traded in August. A 30-year-old right-hander who can become a free agent after next season, Barnes was 1-3 with a 4.30 ERA and nine saves in 13 chances, striking out 31 and walking 14 in 23 innings.
Brasier was 1-0 with a 3.96 ERA in one start and 24 relief appearances, and Brice 1-0 with a 5.95 ERA in one start and 20 relief appearances.
Plawecki batted .341 with one home run and 17 RBIs in 82 at-bats as the backup to Christian Vazquez.