The midfielder opened the scoring after 13 minutes when he put away a Luke Wilkshire cutback from the byline. The Polish defence were unable to keep an eye on the 26-year-old, and he made them pay on the scoreboard.
The lead, though, only lasted five minutes, as Robert Lewandowski ghosted past the Australian defence and slotted his shot home past Adam Federici to equalise.
But the Socceroos restored their lead once again, with Holman threading a ball through the Polish defence to Richard Garcia who was sent sprawling to the ground in the penalty area. The referee had no choice but to point to the spot.
Wilkshire stepped up to take the penalty and sent Poland goalkeeper Przemyslaw Tyton the wrong way and made it 2-1 in the 26th minute.
Australia coach Holger Osieck had clearly seen enough of Holman's good work and subbed him off in the 29th minute for Brett Emerton.
Four minutes later, Poland should have equalised when Jon McKain was ruled to have brought down Jakub Blaszczykowski with a last-ditch challenge. Federici was up to the task, guessing correctly where Lewandowski was going to shoot, and tipping the shot wide.Poland did not give up in the second half, as it continued to press for the equaliser, keeping Australia in their own half for a majority of the time.
Their task was made easier as Emerton was given his marching orders in the 71st minute. He pulled Blaszczykowski's shirt and was shown a yellow card, but the referee believed his dissent warranted a second yellow card.
Poland kept pressing, but could not find a way to goal, as Australia held on for Osieck's maiden victory as Socceroos coach.