Olum missed the opening opportunity for the visitors when he headed wide from a tight angle, but his fortunes changed in the 24th minute as Kansas broke the deadlock.
An incisive passing move resulted in Kevin Ellis playing the perfect ball for Olum, who calmly slotted his effort past Donovan Ricketts.
Soony Saad should have doubled his side's lead just after the hour mark, but the Kansas forward drilled his shot straight at Ricketts inside a crowded penalty area.
Kronberg came to the rescue for Kansas late on by tipping Diego Valeri's curled effort wide to make sure they retained their advantage.
It proved to be a nervy finish to the match for Kansas as Adi once again headed a great chance over the crossbar, and the Timbers were ultimately unable to deny the visitors victory.