Portland (13-10-4, 43 points) earned a third consecutive win while improving its hot streak to 6-0-1 since an Aug. 21 road defeat against expansion Austin FC.
The Timbers' Yimmi Chara also scored just before half-time, his second goal in as many games and his fifth of the season. Asprilla logged an assist on the play.
Danny Musovski scored in the 55th minute for the home team, but LAFC (9-12-6, 33 points) dropped its third straight match and remains four points below the playoff line in Major League Soccer's Western Conference.
The winning goal came after Portland's Felipe Mora took advantage of an LAFC defensive breakdown in the midfield to drive into the penalty box ahead of a lone trailing defender. His shot cannoned off the right post. The ball landed at the feet of Asprilla on the other side of the penalty area, and he fired home a 16-yard half volley inside the far post.
It was Asprilla's eighth goal of the season and third in as many games.
LAFC got nine minutes of stoppage time in the second half to find an equalizer but could not in the end. They put a lot of pressure on the Timbers' defense all night, but could not take advantage of more possession (56.5%), shots (14-9) and shots on goal (4-2).
Portland is now 5-4-4 against LAFC. The Timbers swept the three-game season series against LAFC, taking all three games by 2-1 counts. Adding in two draws last year, Portland is unbeaten in its past five encounters with Los Angeles.