Quintin Laing, Eric Fehr and Alexandre Giroux added goals for Hershey. Frederic Cassivi kicked out 33 shots to record his ninth win.
Brad Moran and Joe Rullier scored for Manitoba.
Moran gave the Moose an early lead, scoring 24 seconds in when he deflected a pass from Lee Goren past Cassivi.
Two minutes later with the Bears on a power play, Wilson grabbed a rebound and sent a shot past Wade Flaherty (20 saves) from just outside the crease.
Laing and Giroux combined on a two-on-one short-handed effort as Laing scored his third of the season. It was Hershey's league-leading 11th short-handed score in 22 games.
Six minutes into the second period, Wilson scored on a backhander while the teams were skating four-on-four, giving the Bears a 3-1 lead.
Giroux picked up another assist when Fehr scored a power-play goal at the seven-minute mark of the third period.
The Moose pulled within two when Rullier scored on a shot from the right point at 11:11 for Manitoba's only power-play score in 10 chances.
Manitoba (10-9-3-2) pulled its goaltender for an extra skater with 1:52 remaining and Giroux scored into an empty net for his team-leading 17th goal of the year.