In a match of few opportunities, the 32-year-old picked up Ahmed Elmohamady's misplaced pass before drilling into the bottom left-hand corner to light up a tepid affair at the Britannia Stadium.
Following victories over West Ham and Aston Villa in Stoke's previous two league encounters, manager Mark Hughes had talked up his side's chances of a top-10 finish for the first time since they were promoted to the top flight in 2008.
However, Stoke did little to back those claims in a first half devoid of clear-cut opportunities, and Hull arguably should have led at the break with Liam Rosenior heading wide when unmarked in the penalty area.
The hosts improved after the break, however, and Odemwingie's individual brilliance ensured a fourth win in five league matches for Stoke, while inflicting a second straight loss on Steve Bruce's men who lost 2-1 at West Ham on Wednesday.
Victory moved Stoke within six points of ninth-placed Newcastle United, while Hull are still looking over their shoulder in 13th, seven points off the drop zone.
The sides proved evenly matched in the opening exchanges, but it was the visitors who fashioned the first chance on goal in the 10th minute as Tom Huddlestone's low 20-yard drive forced Asmir Begovic into a smart stop.
Stoke were then handed a huge reprieve four minutes later when Shane Long hung up a superb cross for the unmarked Rosenior only for the full-back to put his header over the crossbar when he should have at least hit the target.
Hughes' men were somewhat disjointed in the opening half an hour with several misplaced passes curtailing promising attacks, and Odemwingie's scuffed shot from the edge of the box proved to be Stoke's only opportunity of note in a lacklustre first half.
The hosts' showed more urgency in the early throes of the second half, Odemwingie testing Hull's stand-in goalkeeper Steve Harper for the first time before Peter Crouch sliced a half-volley well wide.
Despite the second-half improvement, Stoke were thankful to Begovic shortly before the hour mark, the Bosnian flinging his right hand in the air to prevent David Meyler's deflected shot, the rebound fell to Nikica Jelavic but he side-footed wide off-balance.
That save proved crucial as Stoke moved ahead on 62 minutes. Elmohamady's woeful pass was picked up by Odemwingie who duly punished Hull by waltzing through the defence and rifling past Harper for his third goal in as many Premier League matches.
Stephen Ireland went close to a second in the 75th minute with a stinging drive, yet one goal proved enough to settle the encounter.
