Fochive scored the go-ahead goal in the 68th minute for Portland (11-10-4, 37 points), seven minutes after coming in as a substitute.
A Portland centering pass from the right wing cleared out of the penalty area, but Sebastian Blanco gained possession just outside the top of the box and drove to the end line on the left wing. His cross was deflected at the near post by a Los Angeles defender, then skipped off the turf and across the goalmouth to Fochive, who headed it home from close range.
The Timbers opened the scoring in the 21st minute. Yimmi Chara's corner kick from the left wing pinballed off players from both teams before soaring toward Blanco near the far post. Blanco's header went off the crossbar and back across the goalmouth, and Asprilla headed it into an open net from close range.
Los Angeles tied the score just six minutes later on Arango's penalty kick. It came after Jose Cifuentes' free kick was blocked by Portland's three-man wall.
Referee Chris Penso ruled that the ball had gone off Blanco's elbow as he leaped in the air to block the kick. Arango slowly walked up to the PK and put it into the lower left corner of the net, leaving Timbers goalkeeper Steve Clark no chance.
LAFC nearly took the lead early in the second half as Cifuentes' 40-yard shot sailed over Clark and high off the left post in the 47th minute.
Cifuentes also missed a nearly open net in the 64th minute after a pass from Arango on a two-on-one, shooting wide right from about 10 yards out.
Mora had a goal waved off in the 86th minute because of an offside call.
Clark was credited with one save.