Early goals from Brisbane's Matildas' stars Katrina Gorry and Tameka Butt left the home side with a deserved two-goal margin at halftime on Sunday.
Allira Toby went on at the break and scored just minutes into the second half as the Roar looked set to run away with the contest.
Adelaide, despite missing several key personnel including Brazilian import Monica Hickmann Alves, came back strongly creating numerous scoring opportunities as the match became stretched.
Adriana Jones pulled a goal back on the hour mark, while Sofia Huerta scored from the penalty spot to set up a grandstand finish.
The Roar went into the match with just seven points from five outings, but the win kept the two-time champions in touch with the competition's frontrunners.
Brisbane tackle Canberra United next weekend after the capital's team claimed a stunning 2-1 win over the previously undefeated Melbourne City on Saturday.
"We knew we had to watch Adelaide on the counter-attack, but unfortunately we let them come up with two goals that way," Roar midfielder Gorry said.
"We are definitely going out to beat Canberra next weekend, but it will be a tough match so we will have to prepare."
Meanwhile, Western Sydney Wanderers avoided dropping to last as American forward Katie Stengel scored a last-minute equaliser for a 2-2 draw against struggling Melbourne Victory.
A late goal from rookie winger Kariah White had seemed set to secure all three points for the Victory, who were indebted to new goalkeeper Bethany Mason-Jones for a first-half penalty save.