The singer-songwriter hit the Gobi stage at the vaunted music festival ... playing a few songs before taking a break to speak directly to her audience.

Suki starts by mentioning all of the talented women playing at Coachella ... rattling off names like Sabrina Carpenter and Lana Del Rey -- before casually dropping she's been carrying around her own "amazing lady."

At this point, fans started to shriek -- clearly enthusiastic about Waterhouse's gender reveal -- and, her boo Robert Pattinson was also on-hand for her to make the announcement ... holding hands with Suki before her show while on the festival grounds.

Robert and Suki announced the birth of their baby last week and shared a first look with fans where they covered up her face just last week.

Tons of their celeb fans and friends congratulated the couple in the comments of Suki's Instagram post ... bringing a culmination to a highly publicized pregnancy.

Remember, Suki took the stage in Mexico in November and said she'd worn a sparkly dress to distract from something else she had going on -- pointing to her baby bump.

It ended months of speculation about a possible child for the couple who started dating way back in 2018 ... and later moved in together in London while RP filmed "The Batman."

The couple's stayed out of the limelight for the most part ... though, this baby news seems to have them so excited they just can't wait to share it with the fans.