The win was achieved in extra-time as the teams were locked at 3-3 after 90 minutes, but second half substitute Rantie proved the hero as he fired his side into the next round.
Malmo looked to be heading out of the competition as they trailed 3-1 with 14 minutes to go, before Rantie got his first and Mathias Ranegie added another to send the game into extra-time.
The 21-year-old Rantie then added two more as Malmo pulled clear in the tie and ended up comfortable winners.
"Rantie was a fantastic substitution. It was not just the goals he scored, but also his movement. He was dangerous all the time," said Malmo assistant coach Jorgen Pettersson.
Rantie joined Malmo on a 17-month loan contract from Swedish lower league side Hasselholm after Orlando Pirates decided against signing the Bafana Bafana international at the end of last season.
Meanwhile, Bafana Bafana skipper Steven Pienaar played a starring role for English Premiership Everton as they defeated Manchester United in their season-opener on Monday night.
Pienaar was busy as ever and part of a superb Everton midfield effort that gave The Toffees a deserved victory and a fine start to their season.