Brook had promised a show for his adoring public and he delivered, flooring Saldivia with a right uppercut in the very first round.
Saldivia posed a few problems in the second round when landing a good combination but Brook edged the round.
Early in the third he came out all guns blazing and a straight left connected beautifully to send the Argentine to the canvas again.
This time Saldivia lasted the full 10 count, sparking celebrations in the Brook camp.
He will now face the winner of the title bout between Devon Alexander and Randall Bailey as he gets a shot at the IBF welterweight title himself.
Jamie McDonnell will also have a title bout, in the IBF world bantamweight division, after defeating Darwin Zamora.
Zamora was a late call-up following the withdrawal of Vusi Malinga and he proved stubborn before electing not to get off his stool at the start of the eighth round.