Under OP's scenario, tiebreaker would go all the way to strength of victory, because Cowboys and Eagles would have the same division record (4-2), common opponents record (6-6), and conference record (7-5). According to ESPN's playoff generator, strength of victory tiebreaker would go to Dallas.
That could possibly change, if say, Tampa goes on some crazy win streak (Tampa is a team the Eagles have played and beaten, but the Cowboys won't play), but it's fairly unlikely.
Easiest thing to do is just beat Washington and guarantee that the Cowboys win the division if they finish with the same record as the Eagles.