Jaffray scored the deciding goal at 14:46 of the third. Rookie defenceman Alex Edler had two goals while Lee Goren and Jesse Schultz had the others as Manitoba (16-13-8) rallied from a 3-2 deficit to start the third period.
Tyson Nash, Jamie Sifers and Erik Westrum replied for the Marlies (13-17-4) before a Ricoh Coliseum gathering of 6,246 fans.
Toronto suffered its second straight loss and sixth in a row at home (0-5-1) since beating Milwaukee 4-2 on Nov. 29. The Marlies did have a 3-1 lead Thursday night and took a 3-2 edge into the final period, only to surrender three unanswered goals.
Manitoba netminder Drew MacIntyre stopped 27 shots for the victory while Toronto's Jean-Francois Racine made 26 saves.
The Moose were 1-for-5 on the power play, while the Marlies went 0-for-2 with the man advantage.
The Marlies visit the Hamilton Bulldogs on Friday while Manitoba returns home for a weekend series with the Syracuse Crunch, starting Friday night.