After missing the past two matches with a hamstring strain, Luongo bagged both goals in the victory as the Robins maintained their push for promotion out of League One to the second-tier Championship.
It took a brilliant save from Bradford keeper Jordan Pickford in the second half to deny the 22-year-old Australian a third.
Luongo's first came after in the 15th minute when he took on the defence and smashed the ball into the corner of the net.
He scored the second on 34 minutes when on hand to fire in a loose ball after Andy Williams had collected the ball in the penalty area and sidestepped a defender.
Billy Clarke reduced the deficit nine minutes after the break but he failed to stop the Robins from ending a run of three successive defeats.
Luongo was one of three changes for Swindon as he, Raphael Rossi-Branco and Louis Thompson all started in place of John Swift, Harry Toffolo and Yaser Kasim.
Boss Mark Cooper had high praise for Luongo. He was outstanding first half and he looked a real top talent,” he said after the match. “He could have had his hat-trick.”