With the score tied 4-4, Overbay (3-for-4) led off the bottom of the sixth with a single against Orioles starter Chris Tillman and went to second on a sacrifice bunt by Luis Cruz.
That brought up Nunez, who scorched a grounder up the middle. Overbay crashed into catcher Taylor Teagarden, who couldn't handle the throw from the outfield, scoring the decisive run.
Nunez also had a sacrifice fly for the Yankees, who notched a second straight win against the Orioles.
Andy Pettitte (6-6) earned the win despite yielding four runs (three earned) on nine hits over 6 2/3 innings.
Mariano Rivera tossed a scoreless ninth for his 29th save.
Tillman (10-3) absorbed the loss, surrendering five runs on 10 hits over 5 1/3 frames.