The win saw Hull halt a run of five straight games without a win.
Aina scored in the 58th minute to send Hull into the fourth round of this season’s FA Cup.
It is his first ever goal for Hull since joining them on loan from Chelsea last summer.
At the Etihad, Manchester City came from 1-0 down to thrash Burnley City 4-1 to advance into the next round of the FA Cup.
Burnley took a shock 1-0 lead through Ashley Barnes on 25 minutes off a mistake from John Stones.
But second half goals from Sergio Aguero (56th, 58th minutes), Leroy Sane (71st) and substitute Bernardo Silva (82nd minute) secured the comfortable win for the Premier League leaders.
League Two side Stevenage were forced to a 0-0 draw by Championship club Reading without Nigerian forward Sone Aluko who was benched.
Both teams will meet in a replay to decide who will go through to the fourth round.
Burton Albion were knocked out of this season’s FA Cup following their 1-0 away loss to fellow Championship club Birmingham City.
Nigerian midfielder Hope Akpan was introduced with four minutes left but could not prevent his side from going out.
At Vicarage Road, Watford, without Nigerian forward Isaac Success, made easy work of Bristol City, winning 3-0.
And in another game, Sammy Ameobi was on from the start for Bolton Wanderers who lost 2-1 at home to Premier League club Huddersfield Town.
Ameobi was replaced in the 76th minute of the game.
FA Cup Round 3 results:
Manchester City 4 vs 1 Burnley
Stevenage 0 vs 0 Reading
Blackburn Rovers 0 vs 1 Hull City
Birmingham City 1 vs 0 Burton Albion
Watford 3 vs 0 Bristol City
Bolton Wanderers 1 vs 2 Huddersfield Town