Jerry Palacios and Jonathan McDonald were on the scoresheet for the Costa Rica Primera Division side at the Estadio Rommel Fernandez.
The 2-0 aggregate win puts Oscar Ramirez's Alajuelense – two-time CONCACAF Champions' Cup winners – into a last-four tie against Liga MX side Toluca.
After a 0-0 draw at home, Alajuelense made a dream start in Ciudad de Panama thanks to Palacios.
Palacios diverted a driven Kenner Gutierrez strike part Arabe Unido goalkeeper Alexander Andreve from six yards.
The visitors doubled their lead on 58 minutes to put the tie to bed.
McDonald got on the end of a Johan Venegas cross and his header was too powerful for Andreve, who could only parry the effort into his own net.
The semi-final appearance is a huge improvement by Alajuelense, who failed to get out of their group last season.
