Jason Jaffray scored the eventual winner at the 6:31 mark in the second period, with assists coming from Moran and Lee Goren. Brad Norton registered the Griffins' lone goal.
Moran opened the scoring in the first period on the power play, putting away a feed from Brandon Reid. Maxime Fortunus also assisted on the marker.
Drew MacIntyre gets the win, stopping 21 of 22 shots for Manitoba, while Jimmy Howard blocked 21 of 23 shots for Grand Rapids.
Game 7 goes Tuesday in Winnipeg.