Gameplay Situation I need a ruling on

[Fivesdadda]

Here's the situation...
Two outs, runners on second and third. There's a ground ball hit to short and both runners run on contact. The shortstop throws to third and the third baseman completes the tag play on the runner trying to advance to third for the final out of the inning. The batter-runner didn't make it to first before the tag was made, but for arguments sake we'll say the runner from third did cross the plate before the tag was made. Does the run score? Or does the run not count because of the batter not getting to first and the third out of the inning being made?

Any help and/or references to an official rulebook would be incredibly helpful. Thanks guys.