Both teams are at the wrong end of the table and although Cardiff have seemed revived under new manager Steve Morison, the Bluebirds struggled on home turf.
They conceded a poor first-half goal to Lewis-Potter, who finished from close range.
Hull were neat and tidy in possession in the first 10 minutes, while at the other end 20-year-old Cardiff striker Isaak Davies went on a mazy run before he was tackled.
The Tigers went ahead in the 15th minute when George Honeyman swung in a corner from the left and Ryan Longman flicked on. The ball fell to Lewis-Potter in the six-yard box and he beat Leandro Bacuna to head home.
Cardiff thought they had levelled when Will Vaulks’ long throw ended up in the back of the net. Aden Flint and fellow Bluebirds defender Mark McGuinness had tried to make contact, but no-one got a touch so referee Thomas Bramall rightly ruled the goal out.
The home side had two great chances in quick succession from Ryan Giles and Perry Ng crosses.
Hull came close to a second when they worked a neat set-piece move which eventually found Josh Magennis at the back post. He could only nod against a post when it looked easier to score.
Cardiff: Smithies, McGuinness (Harris 85), Flint, Nelson,Ng, Vaulks (Ralls 46), Pack, Giles, Bacuna (Colwill 63), I Davies (Collins 63), Moore. Unused substitutes: Phillips, Morrison, Brown.
Hull City: Baxter, Greaves, McLoughlin, Elder (Huddlestone 45), Lewis-Potter, Smallwood, Docherty, Longman, Honeyman (Mills 90), Wilks (Williams 66), Magennis (Eaves 80). Unused substitutes: Ingram, Cannon, Moncur.
Referee: T Bramall (Sheffield).