Hoffman headed home a Sebastian Ryall cross in the 14th minute in a period where Australia had nine attempts on goal before Yemen's first shot was saved by goalkeeper Andrew Redmayne on the half hour.
Australia continued to press in the second half before Nichols added his team's second goal in the 67th minute with a close-range shot from a Hoffman cross. Hoffman rounded off the scoring with his second goal and the home team's third in stoppage time.
The winner of the tie advances to the group stage, from which the three group-winning teams will represent Asia in the football tournament at next year's London Olympics.
Men's football is played as an U-23 tournament at the Olympics, although the rules allow for three over-age players.