The visitors nearly took the lead in the 16th minute only for Alhassan to clear off the line following a goal-mouth scramble.
The 22-year-old Ghanaian then came close at the other end, but was left frustrated after watching his shot come back off the post in the 31st minute.
Alhassan did manage to find the net from the edge of the box to put his team in front in first-half stoppage time.
Toronto were a threat from set pieces all evening, but it was the hosts who put the game beyond doubt in the 83rd minute thanks to the tenacity of Valeri.
The Argentine international forced a mistake from the Canadian backline before squaring for Wallace to slide home.
Further goals were added by captain Johnson and Valeri late on, which perhaps flattered the Timbers.
The result means that Toronto remain 10 points adrift of eighth-placed Columbus Crew in the Eastern Conference.