The Cardiff City forward had already had the best chance of the first half – forcing an acrobatic save from Swiss goalkeeper Yann Sommer – but Wales rode the wave of Switzerland pressure to go in level at the break.
Shortly after the restart, the Swiss took advantage of their numerous set-pieces as Breel Embolo nodded home from Xherdan Shaqiri’s corner.
But Wales began to fashion chances and they scored in somewhat similar fashion as Joe Morrell sent in a cross after a short corner and an inexplicably unmarked Moore glanced a header past Sommer.
There was late drama in Azerbaijan too as VAR ruled out Mario Gavranovic’s late strike for offside, mere seconds after the forward had come on as a substitute.
Switzerland pushed for a winner in the final minutes, but Wales held out for what could be an important point in Group A, which is topped by Italy after their 3-0 victory against Turkey on Friday evening.
Wales are next in action on Wednesday when they take on Turkey, once again in Baku, kick-off 5pm. Switzerland will now travel to Rome to take on Italy, also on June 16, kick-off 8pm.