With 1 out and runners on 3rd and 1st, the hit and run is on, so both runners are aggressively stealing on the pitch.

 

The batter hits a pop-up that is caught by the 2nd baseman. The 2nd baseman then chases down the runner that was going from 1st to 2nd and tags him for the third out of the inning. However, that third out is recorded well AFTER the runner from third crossed home. 

 

This 3rd out is a timing play (as we learned in class), but does the run that scored from 3rd count (since that runner very clearly ran directly home on the pitch and failed to properly tag up on the pop-up)?