The Lions trailed by 17 points at the final change but kicked three unanswered goals in the last quarter of their 6.5 (41) to 6.2 (38) victory at Norwood Oval on Sunday.
Crows midfielder Teah Charlton gifted Smith a simple shot at the top of the goal square when she was penalised for a late push on Shannon Campbell.
Smith converted the chance with little more than a minute left and Brisbane hung on in the desperate final stages.
Charlton was in tears after the siren and had to be consoled by teammates.
"It was the hard work of the girls up the field and I was just the lucky one to get it down the field," Smith told Seven of her match-winning goal.
"We love playing Adelaide. They're great competitors and really classy opposition.
"We've all got to know them pretty well now, so we just enjoy the competition and enjoy the fight."
The result extended Brisbane's dominance of their fellow AFLW heavyweights to 11 wins from 14 meetings.
Six of those clashes have been decided by margins of one goal or less.
The latest battle was played with a finals-like intensity from the outset, with the hosts on top early.
Adelaide kicked the first two goals, including a brilliant Eloise Jones strike from the boundary line after she beat Sophie Conway to a loose ball.
The lead changed four times in an entertaining second term and the Crows looked to have built a match-winning margin in the third when they kicked 2.1 to 0.1.
Goals to Courtney Hodder and Charlotte Mullins dragged Brisbane back into the contest in the last quarter and tempers flared with the game on the line.
Adelaide star Chelsea Randall caught Hodder holding the ball and the Lions goalsneak was furious, shoving several opponents and giving away a 50-metre penalty.
The game went down to the wire and Smith stood up in the decisive moment, with Brisbane holding their opponents scoreless in the final term.
Smith, Hodder and Mullins finished with two goals each for Brisbane, while Ally Anderson (22 disposals), Jade Ellenger (22) and defensive rock Bre Koenen (18) were influential.
Randall kicked two majors for Adelaide, who were well served by gun midfielder Ebony Marinoff (23 disposals, five clearances).
The result left Brisbane and Adelaide with 2-2 records after four rounds.
12°C