David Meyler and summer signing Andy Robertson were on target for Steve Bruce’s side, with Vedad Ibisevic offering a solitary response for the hosts.
With the start of the new Premier League campaign now less than a week away, Hull are busily finalising their plans for an opening day showdown with Queens Park Rangers.
They have already taken in competitive football this summer, with Europa League qualifiers helping to get them up to speed.
Bruce opted to rest all of those used in a tie with Trencin when naming his starting XI in Germany on Sunday, but saw a much-changed side get off to the perfect start.
There were just five minutes on the clock when the deadlock was broken, with Meyler powering home from the edge of the box following a shambolic clearance from Sven Ulreich.
Seven minutes later and Hull doubled their lead as Robertson followed up to convert from a tight angle after Nikica Jelavic had seen a header beaten out by Ulreich.
Further opportunities to build on that lead were squandered and Stuttgart were offered an opportunity to halve their deficit when Maynor Figueroa hacked down Martin Narnik inside the box.
Veteran goalkeeper Steve Harper was equal to Ibisevic’s spot-kick, though, and Hull preserved their two-goal cushion.
That lasted until six minutes before the interval when Ibisevic finally found the back of the net with a composed finish from 20 yards out.
Both sides had their chances after the break, most notably through Tom Ince, but there were to be no more goals and Hull head home hoping for more of the same at Loftus Road on Saturday.