Attacking ace Aluko swept in a low left-footer for his fifth goal of the season to keep Steve Bruce's Tigers in the Championship play-off places.
Barnsley were very much second best despite the slender scoreline and look set for another battle against relegation.
While Barnsley did not manage a shot on target in the opening half, the Tigers should have put the game to bed before the break.
City got their noses in front after 16 minutes when Ahmed Elmohamady's ball into the box was only half headed clear by John Stones and fell to Aluko, whose low left-footed shot from 15 yards appeared to pick up a slight deflection off Scott Wiseman on its way past Luke Steele.
Hull kept pressing and in the 21st minute Elmohamady met Robert Koren's inswinging corner but sent his eight-yard header over the top.
Koren then had an edge-of-the-box effort parried by Steele after 32 minutes before the Barnsley keeper pulled off an even better save to keep out a close-range header from Corry Evans.
Six minutes into the second half Liam Rosenior should have done better with a shot from six yards that he lifted over the top.
Barnsley did show more attacking intent in the second period but struggled to create any clear-cut opportunities to test Hull keeper Ben Amos.
They sent on former Liverpool winger Toni Silva for his debut but their best effort was a 65th-minute shot from Polish midfielder Tomas Cywka that flashed just wide.
And it was left to Steele to keep the margin of victory down to one goal, as he pulled off another top-class parry to thwart striker Jay Simpson in the 78th minute.