United – decimated by injuries and players on holiday – had a 10th minute chance when Callum Anderson rose unchallenged following a corner but his header was comfortably saved.
East Kilbride then headed a scoring opportunity over at the other end.
Lanark continued to look dangerous in attack and Ben Elliot got to the left byeline before crossing for James Martin, but the ball would not sit kindly for Martin and the
danger was cleared.
On the half hour mark the visitors broke well on the right but a decent stop from Lachlan Kirkland kept the scores level.
The final action of the half for the home side came when a long ball found Andy Gilchrist who put a decent ball into the box but there were no takers.
Lanark had their best chance of the match two minutes into the second half when Fraser set Elliot free but his parting shot was well saved by Munoz.
A great ball from Gregor Henderson then picked out Martin, who in turn laid the ball into Fraser but his shot went wide of the target.
With 10 minutes of the second half gone East Kilbride almost took the lead in controversial circumstances when the referee got in the way of Fraser in midfield, with the ball breaking kindly for East Kilbride. It took a good double save from Kirkland to keep them out.
The deadlock was eventually broken in the 78th minute when Lanark lost possession after their throw in and East Kilbride played a couple of passes before Edgar hit a low shot that beat Kirkland low to his left.
This goal knocked the stuffing out of Lanark and they lost a second goal on 85 minutes when a corner was poorly defended and Kidd hammered home for 2-0.
Lanark: Kirkland, Henderson (McGuire), Lawson, Doran, C Anderson, Fraser, Gilchrist, McArdle, Wilson (Smith), Martin, Elliot.
United return to league duties this Saturday with a home Conference C game against St Anthony’s, KO 2pm.