Kristine Lilly scored 10 minutes into the second half to extend the Breakers' lead.
The Breakers, who had given up four goals in a 4-0 loss at Chicago a week earlier, held Marta scoreless. The Sol's only goal came when Brittany Bock deflected Aya Miyama's pass off her body.
With the win, Boston moved into second place, one point ahead of Chicago, WPS's only unbeaten team, and one behind Los Angeles, which was scored upon for the first time in five games.
"I am really proud of the players because they were embarrassed last week," said Breakers coach Tony DiCicco. "They played the No. 1 team in the league who hadn't lost a game or given up a goal, and I am very proud of the showing we had. The key to the game was mentality. I thought we started well in both halves, but Los Angeles is a very good team."
Los Angeles coach Abner Rogers said the Sol needs to find Marta in dangerous positions.
"There were times when she was coming too deep to get the ball and then we couldn't get enough people into the attack," he said. "It's early in the season, though, and I think we'll start to fuse things together and see the best of everyone towards the end of the season.
Saint Louis Athletica, which was scoreless in its first three games, looked to be headed to its first win, taking a 3-1 win at Washington, but the Freedom rallied for two late goals, one by Australian Lisa De Vanna in the 79th minute and the other by Frenchwoman Sonia Bompastor, her second goal of the game, in the 90th to earn a 3-3 tie.
Brazilian Daniela scored twice for St. Louis, and Englishwoman Enoila Aluko had the third goal. Daniela was later stretchered off and looked to have suffered a serious injury after an Abby Wambach tackle.
Sub Leigh Ann Robinson's goal in the 86th minute gave FC Gold Pride a 1-0 victory over winless Sky Blue FC in a match that drew only 2,533 fans -- the smallest crowd for a WPS game -- at Buck Shaw Stadium.
May 2 in Cambridge, Mass.
Boston 2 Los Angeles 1. Goals: Smith (Schmedes), 2, Lilly (Bishop), 55; Bock (Miyama), 63.
Boston - Luckenbill, Scott, LePeilbet, Weber, Mitts, Smith, Hucles, Bishop, Schmedes (Moore, 75), Latham (Rodriquez, 64), Lilly.
Los Angeles - LeBlanc, Bock, Cox, Franko, Makoski, Wagner, Boxx, Miyama, Abily (Larkin, 74), Marta, Duan.
Referee: John Schmitz.
May 3 in Santa Clara, Calif.
FC Gold Pride 1 Sky Blue FC 0. Goal: Robinson (Adriane) 86.
FC Gold Pride - Barnhart, Dew, Buehler, Graczyk, Formiga, Milbrett (Arakawa, 57), Osborne, DiMartino, Sinclair (Robinson, 70), Weimer (Adriane, 84), Wilson.
Sky Blue FC - Branam, Sitch, Asante, Dowling, Rampone, McCallum (Kai, 45), Parker, Schnur, Averbuch (White, 80), Walsh (Rosana, 65), O'Reilly.
Yellow Card: Sky Blue FC - Parker 44.
Referee: Felisha Mariscal.
May 3 in Germantown, Md.
Washington 3 St. Louis 3. Goals: Bompastor (Gilbeau) 29, De Vanna (Wambach) 79, Bompastor 90; St. Louis - Daniela 7, Daniela 41, Aluko (Hanks) 69.
Washington - Spisak, Gilbeau, Sauerbrunn, Whitehill, Singer, De Dycker (Moros, 64), Lindsey, Sawa, Long (De Vanna, 46), Wambach, Bompastor.
St. Louis - Solo, Francielle, Ellertson (Cross, 74), McNeill, Weber, Stoia, Woznuk, Daniela (Gray, 83), Chalupny, Tancredi (Hanks, 67), Aluko.
Yellow Cards: Washington - Wambach 81; St. Louis - McNeill 39, Weber 90.
Referee: Shane Butler.
TEAM W L T GF GA P
Los Angeles 3 1 1 6 2 10
Boston 3 2 0 8 8 9
Chicago 2 0 2 6 1 8
FC Gold Pride 2 2 1 7 7 7
Washington 1 2 2 9 12 5
St. Louis 0 2 2 3 6 2
Sky Blue FC 0 2 2 1 4 2
Kelly Smith (Boston) 4
Marta (Los Angeles) 3
Daniela (St. Louis) 2
Lori Lindsey (Washington) 2
Kristine Lilly (Boston) 2
Tiffeny Milbrett (FC Gold Pride) 2
Lindsay Tarpley (Chicago) 2
Sonia Bompastor (Washington) 2
Abby Wambach (Washington) 2
Saturday, May 9
Saint Louis vs. FC Gold Pride, 8 pm ET
Sunday, May 10
Los Angeles vs. Boston, 4 pm ET
Chicago vs. Sky Blue FC, 6 pm ET (FSC)