New signings Ella Rutherford and Charlie Devlin started for the Foxes for their first outing of the 2020 campaign, but it ultimately ended in disappointment for the visitors.
Lachante Paul and captain Holly Morgan both carved out half chances for City early on, while Nat Johnson needed to hook the ball off the line at the other end.
Kathryn Hill and Molly Sharpe also went close for the home side before the latter eventually put Durham ahead on the half-hour mark, finishing well from over 30 yards out.
The Foxes pushed for an equaliser in County Durham but were unable to create chances as the third-placed hosts sealed a ninth win in 12 matches this season.
Leicester, sat ninth in the 12-team league standings, will next be in action away against Crystal Palace at Hayes Lane on Sunday (2pm GMT kick-off).
The details...
City: Lambourne, N. Johnson, Morgan (c), Cataldo, Devlin, Paul, James, Thomas, Bailey-Gayle, Brown (Blanchard 63'), Rutherford (Smith 72')
Subs not used: Field, Everett, Atkinson, Camwell