Victory in Lancashire gave Hull a third straight win on the road and they will be full of belief that they could be in contention for the automatic promotion places.
After an even opening half-an-hour they took the lead from a Preston corner.
The hosts used a clever routine to free up a shot on the edge of the area but the effort was blocked and the Tigers quickly released Akintola down the right and he sped away unchallenged before teeing up ex-North End loanee Millar to convert from close range.
The visitors doubled their lead just before the break when McBurnie showed good composure to lay the ball back for Famewo to finish smartly for his first goal for the club.
Preston boss Paul Heckingbottom brought on Lewis Dobbin, Daniel Jebbison and Jamal Lewis at the break but they had next to no time to make an impact before the game was put beyond the home team.
The Tigers were forced into a change of their own just after the restart when Akintola went off with a knock and debutant Yu Hirakwa had an immediate impact.
The Japan international joined on loan from Bristol City on Monday and his first act in a Hull shirt saw him race after a loose ball and cross in for McBurnie to stylishly volley in.
Jakirovic was able to bring on joint-top scorer Joe Gelhardt for his first appearance since 5 December and he forced a save out of Christian Walton as they went in search of more goals.
Montenegro international Osmajic was sent off in the final seconds of the match for a ridiculous headbutt on sub Lundstram after the pair had come together after a foul.
Hull will look to continue their promotion push when they host Swansea on Saturday, while Preston will look to get their top-six bid back on track when they travel to Middlesbrough on the same day.