Asmir Begovic saved a Tom Huddlestone shot and Liam Rosenior headed over as Hull could not find the breakthrough in the first period.
Begovic then made a fantastic save after the break to deny David Meyler's deflected shot and Hull were made to pay when Odemwingie struck in the 62nd minute.
The Stoke striker fired in from the edge of the box after collecting the ball from a stray Ahmed Elmohamady pass to register his fourth goal in three games, and fifth since joining the Potters from Cardiff in January.
Mark Hughes' men held on to make it three wins on the bounce and reach the magic 40 points mark, while Hull remain on 33 points and in relegation trouble after their fourth defeat in five Premier League matches.
The Potters look safe with six more games to go and are finishing Hughes' first season in charge strongly, having lost only one of their last nine matches and winning four of their last five.
They are 10th in the table and their hopes of improving on their best Premier League final position of 11th and points tally of 47 this term is looking increasingly realistic.
There has been considerable enthusiasm about Stoke's results and performances of late - particularly their 4-1 win at Aston Villa last weekend - but there was little to get excited about in a scrappy first half of this encounter.
After Peter Crouch headed wide from a corner early on, Huddlestone threatened at the other end, bringing a diving save out of Begovic with a drive from outside the box.
Moments later a decent opportunity went begging for the visitors when Rosenior, finding space in the Stoke area, connected with Shane Long's cross but could only direct his header over the bar.
Odemwingie struck an optimistic effort from distance that bobbled wide after some patient Stoke build-up play just before the half-hour mark, and in the closing stages of the half the Nigerian squared to Marko Arnautovic, whose scuffed shot was easily collected by Hull keeper Steve Harper.
Stoke looked to up the tempo after the break and Odemwingie lashed an attempt goalwards that Harper got behind, before Crouch skewed wide with a shot on the turn.
The Potters then breathed a sigh of relief when Meyler's deflected strike from outside the box looped towards goal and Begovic did well to palm it away, the ball subsequently going wide with Nikica Jelavic unable to make anything of the rebound.
Six minutes later, Stoke had the lead as Odemwingie capitalised on Hull midfielder Elmohamady's misjudged cross-field ball, intercepting it, driving forward, getting past Curtis Davies and cracking the ball home.
Hughes' side continued to press and Arnautovic burst through and saw his shot blocked by Rosenior.
Stephen Ireland's effort was then pushed over by Harper as Hull kept the scoreline to a single goal.