Diomansy Kamara grabbed his first Fulham goal to send his new side into the Carling Cup third round.
The visitors dominated the early stages, Kamara hit the bar with a header from David Healy's cross and Carlos Bocanegra fired wide.
Simon Davies also tested Shrewsbury keeper Ryan Esson with a fierce shot while Jimmy Ryan went close with a clever chip for the home side.
Fulham settled the tie when Kamara headed in following a Davies corner.
Shrewsbury: Esson, Moss, Kempson, Murdock, Tierney, Humphrey, Hunt (Hall 69), Ryan, Leslie, Hibbert (Onibuje 68), Symes.
Subs Not Used: MacKenzie, Langmead, Clancy.
Fulham: Warner, Volz (Omozusi 79), Pearce, Bocanegra, Konchesky, Davies, Smertin, Davis, Dempsey, Healy (John 75), Kamara.
Subs Not Used: Ricardo Batista, Diop, Watts.
Booked: Pearce, Kamara, Omozusi.
Goals: Kamara 59.
Ref: Paul Taylor (Hertfordshire).