Andranik came close to handing Fulham the lead in the first-half after his long-range effort took a deflection.
The Whites notched their first of the evening on 13 minutes when Kallio rose high in the box to head past Liam O'Brien from a well-delivered corner.
The Whites doubled their lead just before the half hour mark when Michael Uwezu was allowed the space to finish from Matt Saunders' corner delivery.
Eddie Johnson twice came close to finding the net before the half-time but he was denied on both occasions by some desperate defending.
The Whites maintained their control of the game in the second-half with Joe Anderson having the best of the Fulham chances. But Pascal Zuberbuhler was rarely called upon as Fulham saw out the rest of the match well in control.
Fulham Reserves: Zuberbuhler; Brown, Kallio, Anderson, Smith; Uwezu (Hoesen 70 - Jones 90), Andranik, Saunders, Seol; Johnson (Marquez-Sanchez 90), Elm
Portsmouth Reserves: O'Brien; Suric, Williamson, Wilkinson, Hurst; Basinas, Diop (Bopp 75), O'Hara (Apicerni 63), Hughes; Piquionne, Webber (Samba 46)
Read more: http://www.fulhamfc.com/Club/News/NewsArticles/2009/October/ReservesvPortsmouth.aspx#ixzz0lHGYi8nz