Both teams went close with two good chances each in a blank first half before Williams struck with 17 minutes remaining.
Racing onto a ball pulled back into his path by Neil Hughes, he made no mistake from 12 yards.
Queen's Park were unlucky to see a shot from Ed Morris Jones hit a post and Kevin Leach also hit Llandyrnog’s bar.
David Ross Williams might have added a second, but his effort was cleared off the line.
