Forrest head coach Babe Hardison, who is retiring at the end of the season, was honored before the game on Monday.
Hardison has coached the Rockets since 1986, compiling a record of 483-261, with his best finish coming in 2006 when the Rockets placed second in Class A.
Boyce went the distance on the hill for Moore County, giving up seven hits, while striking out seven and walking two Rocket batters in the contest.
The Rockets had their first chance to get on the scoreboard in the bottom of the second, beginning with senior Richard Hardin's one-out single to right field.
Austin Harmon came in to courtesy run for Hardin and promptly swiped second base.
Ryan Daughrity followed with a walk before Boyce got out number two on a strikeout.
Jacob Daughrity hit a hard grounder to short and the throw to get Daughrity was high, but bounced perfectly off the fence where Dakota Bateman scooped it up and nailed Harmon at home for the final out of the inning.
Forrest would get two on with two out in the bottom of the third, and once again Bateman saved the day with a pretty scoop of a low thrown ball to first for out number three.
Brewer would face some trouble in the top of the fourth as he walked Boyce and Cole Montgomery before striking out the side in order to escape the threat.
A Ryan Daughrity one-out ground-rule double in the bottom of the inning was wasted as Boyce got a pop-up to second, followed by a grounder to short to escape unscathed.
Tanner Garvin came to the mound for Forrest in the fifth and gave up a lead-off single to Justin Durm.
Durm stole second and was sacrificed to third on a bunt by Bateman.
Bateman would score moments later on a wild pitch, making it 2-0 before Garvin got out of the inning.
Forrest threatened again in the home half of the inning as Austin Harber doubled to left and Zach Horvath followed with a single to put Rocket runners on second and third.
Harber could not tag and score on a shallow fly to right and the inning ended on a grounder to Bateman at first.
Garvin set down the Raiders 1-2-3 in the sixth and the Rockets got a lead-off single by Hardin in the bottom of the frame to set up a comeback try.
After Ryan Daughrity just missed a game-tying homerun to left, Garvin reached on an error to put runners on first and second with one down.
Boyce would have none of it, whiffing the next two Forrest hitters to send the game to the final inning.
Ryan Daughrity came to the hill for the seventh and issued a two-out base on balls to Durm, but he was cut down trying to steal on a perfect shot to second by Hardin.
Harber lashed his second hit of the night, leading off the home portion of the inning, but was erased at second on a 6-4 fielder's choice off the bat of Horvath.
Brewer kept hope alive for the Rockets with a single up the middle and both runners advanced to second and third on a passed ball.
Paten Pruitt knocked in Horvath on a sacrifice fly, but the Rockets' hopes faded on a ground ball to short to end the game.
Forrest (3) lost 6-3 in nine innings to Middle Tennessee Christian School (6) in the first round of the District 9-A Tournament in Chapel Hill on Thursday and will play in the loser's braket on Saturday.