Barrichello edged Schumacher by five-hundredths of a second Saturday with a time of one minute, 25.843 seconds at the 3.295-mile Albert Park circuit during a one-hour qualifying session that was cut short due to rain.
The Ferrari's took the front row despite using last year's car. The Brazilian is a strong driver in wet conditions and won his only race in similar conditions in Hockenheim in 2000.
Schumacher was pleased, despite failing to capture his 44th career pole.
"Two Ferraris on the front row is the best possible start to the season and we are delighted with that," said the German, who has won the championship the last two seasons. "We know our car very well, which obviously helped our performance today."
Schumacher's younger brother, Ralf, took the third spot in his Williams BMW, ahead of the McLaren-Mcercedes drivers David Coulthard of Scotland and Kimi Raikkonen, who is replacing two-time F1 champion Mika Hakkinen.
Williams driver Juan Pablo Montoya of Colombia will start from sixth place, followed by Jarno Trulli's Renault and the Jordan-Honda of Giancarlo Fisichella of Italy.
Celebrity Couples of 2014 [PHOTOS]