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.
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