Kuwait defender Mesaed Alenzi gave the visitors the lead after 37 minutes then helped his team mates hold firm against a wave of attacks.
The Australians, fielding a weakened team made up of players from the fledgling domestic competition, struggled to create clear chances then wasted the few opportunities they did get.
Striker Archie Thompson missed a golden chance from two metres early in the first half, then his Melbourne team mate Tom Pondeljak hit the post from a tight angle.
"It's not a disaster but it was very disappointing," Australia coach Pim Verbeek told reporters. "In these sorts of qualifying competitions, you need to win your home games, so this just makes it harder."
Kuwait, who lost their opening qualifier against Oman, scored against the run of play when the unmarked Alenzi darted into the penalty box and headed the ball past goalkeeper Eugene Galekovic.
Kuwait spent most of the next hour defending but almost doubled their lead in the final minutes when substitute Khaled Matar launched a counter-attack only to see his low drive strike the woodwork.
"Australia, away from home, we thought this game would be too difficult," Kuwait's Jarah Alateeqi said.
"We were lucky tonight to score the goal but we played well and we are very happy with the three points."
The result gave Kuwait three points from two matches, one point behind Oman. Indonesia, who held Australia to a scoreless draw in January, have two points and the Socceroos one.
The top two teams from the group qualify for the 2011 Asian Cup in Qatar.
