The Bears, which defeated Riverdale 8-1 on Monday, claimed their fourth consecutive subregion win.
Griffin (9-3 overall, 4-0 Region 4-AAAA North) jumped out to a 1-0 lead after the first inning with a run scored by Xavier Randolph on an RBI single by Jeremy Holcomb.
The Bears added three runs in the bottom of the second inning as Beckham and Randolph connected on back-to-back RBI triples to score Henteves Jester and Beckham. Randolph also scored on a North Clayton error to put Griffin up 5-0.
The Eagles (6-9, 2-5) got a run in the top of the fourth inning to cut the lead to 4-1, but it would be all the offense North Clayton could produce as Griffin starting pitcher Cash Barnhart threw a complete game for the win.
Barnhart allowed one run on four hits and struck out three batters in seven innings of work.
Griffin posted two more runs in the bottom of the sixth inning as Jester and Beckham hit back-to-back triples to score Jester for the second time in the game. Beckham would come home on a sacrifice fly by Randolph.
Griffin continues its season on Friday when the Bears travel to Lovejoy (5-7, 3-1) for a subregion game.