Perez got underneath a ball launched by David Ferreira and headed home the game's only goal for Dallas (4-1-1), which has won four of its first six games this season.
Dallas' Jackson missed what looked to be a sure goal and Ferreira was denied by New England goalkeeper Bobby Shuttleworth just before halftime, but Dallas kept up the pressure after the break.
The Revolution (1-2-2) had their best opportunity on Juan Toja's shot at the near post late in the game, but it was blocked by Dallas goalkeeper Raul Fernandez.
Jeb Bush 'thinking about running for president' in 2016
Humongous iceberg slowly drifts away from Antarctica