Ben Simon put Syracuse ahead 3:12 into the match, but Yannick Tremblay replied on the power play for the Moose late in the period to send the teams into the intermission tied at a goal apiece.
Lee Goren gave the Moose the lead at 5:24 of the second period and Jason Jaffray made it a two-goal margin 37 seconds later for Manitoba (17-13-5-4).
Just over a minute elapsed before Mark Hartigan cut the deficit to a goal and Jeffrey Szwez tied it 51 seconds later for the Crunch.
But Moran's goal was the last of the night and moved the Moose to within a point of second-place Hamilton in the North Division.
Drew MacIntyre stopped 17 of 20 shots in net for Manitoba, but was replaced 8:00 into the second period by Wade Flaherty who made a dozen saves to earn his ninth win of the season.
Tomas Popperle made 24 saves in a losing cause for Syracuse (10-21-1-2).