Host Boston won its fourth in a row as Johnnie Walton threw two touchdown passes in the first 5:22 and Tim Mazzetti kicked two field goals.
Birmingham scored in the second quarter on a two-yard run by Cornelius Quarles and a 22-yard field goal by Scott Norwood, but trailed, 20-10, at halftime.
Two more field goals by Norwood cut Boston's lead to 20-16 with 9:50 left. But Walton led the Breakers on a 10-play, 75-yard drive that ended with a two-yard touchdown run by Tony Davis with 3:52 left.
The Breakers (4-1) broke a first-place tie in the Atlantic Division with Philadelphia, which will host Washington Sunday. The Stallions are 2-3.
On Boston's first possession, Walton threw on a screen to wide receiver Nolan Franz, and Franz ran up the right side behind three blockers for a 26-yard touchdown.
Woodrow Wilson intercepted Bob Lane's pass on Birmingham's first series, but Boston's Joe Restic had to punt from his 31-yard line. The kick hit Birmingham's Johnny Dirden in the back and M.L. Carter recovered for Boston at the Stallions' 12.
This time, Walton threw to Richard Crump coming out of the backfield, and Crump ran 12 yards to put Boston ahead, 14-0.
Quarles' touchdown ended an 80-yard drive. Norwood's first field goal came after Birmingham took the ball at the Boston 41 after a poor punt by Restic.
Mazzetti made field goals of 42 and 23 yards in the final minute of the first half to extend his streak of successful kicks to nine.