The Trail Blazers had lost 14 of their last 16 road contests, but dominated this one while handing Chicago its sixth loss in eight games.
Portland built a 28-point lead before Chicago made the final score representative.
Aldridge had 28 points and Lillard contributed four rebounds and seven assists to go with his 24 points. Lillard made four of Portland's 10 successful 3-point shots.
Joakim Noah led the Bulls with 18 points.
Portland put together a 22-6 run in the second period to break the game open and outscored the Bulls in the middle two periods 60-32.
The Trail Blazers defeated the Bulls in both their meetings this year.