Bower took over the Hornets after a 3-6 start led to the dismissal of Byron Scott.
Not only did New Orleans lose again, but All-Star point guard Chris Paul left the game in the third quarter with a sprained ankle.
Aldridge scored 20 points and grabbed 13 rebounds. Portland inched in front during the final two quarters after owning only a four-point halftime lead.
Brandon Roy added 15 points with eight assists for Portland, which has won five straight games.
New Orleans got 20 points from Marcus Thornton and 15 from David West.
The teams combined to shoot just 10-of-46 from the field in the first quarter, which ended with Portland owning a 14-12 lead.