Goals from Eddie Nkeitah, Gaetano Berardi and Mateusz Klich in a 15-minute stretch spanning the end of the first half and beginning of the second powered the Championship side into round two.
Leeds open Cup campaign with thundering result
Salford started as the brighter of the two sides as Richard Towell saw his shot headed away by Jack Clarke and Leeds goalkeeper Kiko Casilla saved low from Jake Beesley.
The visitors weren't getting many clear-cut chances, often shooting from distance, the pick of the bunch when Ammies goalkeeper Chris Neal stopped Clarke's effort.
Finally, the Whites made their domination count and went in front. Helder Costa whipped in a cross that found Nkeitah, the Arsenal loanee sneaking past the Salford defense to fire past Neal two minutes before halftime.
Danny Whitehead had a go for the hosts, but his shot was deflected out for a corner. The Salford defense, so resolute for most of the game, were to be fatally exposed.
The lively Nkeitah was applying the pressure on the home side and he forced a corner which Costa took on the right. The ensuing result saw Berardi turn past Neal and give Leeds a 2-0 lead in the 53rd minute.
Whitehead twice forced good saves out of Casilla, the best passage of play by Salford, the second resulting in a corner that came to nothing.
It soon became a three-goal lead for the visitors, Klich galloping onto the ball in the Salford half, ignoring Nkeitah's pleas to pass him the ball and beating Neal to effectively put the contest to bed.
The Ammies didn't give up and Adam Rooney somewhat tested Casilla, but it was not nearly enough to trouble the Whites on this night as they emphatically marched into round two.