Hull breezed into the second round of the Carabao Cup after securing a 3-0 victory over Tranmere at Prenton Park.
Ryan Tafazolli headed home a third just before the break and despite a spirited second-half performance from Rovers they could not take one of their numerous chances.
The hosts gifted the initiative to their Championship opponents immediately from kick off.
Soon after, Davies repelled a fierce shot from Josh Magennis but the Rovers defence failed to mop up the loose ball, allowing Milinkovic to bundle home at the second attempt.
Hull notched a third and effectively ended the contest a minute before the break when Tafazolli headed home a Milinkovic corner from inside the six-yard box.
The impressive Corey Blackett-Taylor smashed the crossbar from 30 yards for Rovers after the break but they could not find a way back into the match.