The Cardiff City striker was recalled to Wales' starting line-up for Saturday's clash and justified interim boss Rob Page's selection call by earning his side a crucial point.
Switzerland had won their previous six games and were on course for another victory when Breel Embolo guided in Xherdan Shaqiri's corner early in the second half.
However, Vladimir Petkovic's side could not hold on and were further frustrated late on when substitute Mario Gavranovic had a goal ruled out for offside.
Wales started the match brightly and went close to opening the scoring 15 minutes in through a Moore header that Yann Sommer did well to push over the crossbar.
Danny Ward was called into action up the other end to deny Fabian Schar after the centre-back turned Shaqiri's corner on target with a smart flick.
Switzerland soon took control of possession and squandered another big chance before half-time when Haris Seferovic fired off target from seven yards once teed up by Embolo.
The two men combined early in the second half as Seferovic played in his team-mate to race through and force Ward into a second big save of the contest.
However, Embolo held off Connor Roberts from the subsequent corner and headed Shaqiri's delivery past Ward into the bottom-left corner.
Kevin Mbabu scuffed wide from a good position and Switzerland struggled to make more of their possession, which would come back to haunt them 16 minutes from time.
Joe Morrell sent in a cross from the right and Moore, a presence at both ends of the field throughout, glanced a header in to get Wales off the mark.
Gavranovic thought he had won the game for Switzerland moments after being introduced from the bench, but his left-footed strike was ruled out.