Free throws at end of game

[bballref3966]

I can't seem to find a case play or rule to definitively make a decision, but here's my play...

Team A is down 2 as time is running out in the fourth quarter. A1 is fouled in the act of shooting and misses the shot, but the foul occurred so near the expiration of time that the clock could not be stopped. My question: Are both free throws awarded no matter whether the first is made or missed? Or do we only shoot as many free throws necessary to decide the outcome of the game, thus if A1 missed the first, the game would be decided and ended without a second attempt?