Yankees vs. Red Sox: The End Games

The Red Sox remaining games at home through the end of the season

Orioles -- 3 games -- home record vs. Orioles this season: W4-L2
Blue Jays -- 3 games -- home vs. Blue Jays: 2-4
Devil Rays -- 3 games -- home vs. Devil Rays: 5-1
Yankees -- 3 games -- home vs. Yankees: 4-2
Athletics -- 2 games -- home vs. Athletics: 1-1
Twins -- 4 games -- home vs. Twins: no games

The Red Sox away

Orioles -- 4 games -- away vs. Orioles: 3-2
Blue Jays -- 3 games -- away vs. Blue Jays: 5-1
Devil Rays -- 3 games -- away vs. Devil Rays: 4-2

The Yankees at home

Devil Rays -- 3 games -- home vs. Devil Rays: 4-2
Mariners -- 3 games -- home vs. Mariners: 2-2
Orioles -- 3 games -- home vs. Orioles: 2-4
Blue Jays -- 4 games -- home vs. Blue Jays: 3-2

The Yankees away

Royals -- 3 games -- away vs. Royals: 3-1
Blue Jays -- 3 games -- away vs. Blue Jays: 3-3
Red Sox -- 3 games -- away vs. Red Sox: 2-4
Devil Rays -- games -- away vs. Devil Rays: 3-3
Orioles -- 3 games -- away vs. Orioles: 2-4

Combined home and away records against remaining opponents

Red Sox: 28-15
Yankees: 24-25

Current standings

Red Sox lead Yankees by 5 games

Conclusion

Draw your own, bearing in mind that "past performance is no guarantee of future results."