The victory makes it an impressive four wins from four, and as many clean sheets, in the WSL for the Reds so far this campaign.
Nikita Parris's first-half headed goal, from Katie Zelem's free-kick, proved to be the difference maker for United, who remain level at the top of the league table with Arsenal.
A relatively quiet second half saw both sides have a handful of chances, but Parris's header - and a resilient defensive display - were enough to seal the three points for Skinner's side.
The opening half was relatively even from the off, prompting Leicester to have the first effort on goal through Jemma Purfield.