Robert Irwin 's emotional dance on "Dancing with the Stars" left no dry eyes in the ballroom ... as he paid homage to his mother.

The 21-year-old and his partner took the floor to Phil Collins' "You'll Be in My Heart" ... all part of the show's "Dedication Night," when celebs pay tribute to someone special.

In his confessional, Robert explained how his mom, Terri , "always made sure my dad was present in our lives" ... opening up about how he struggled after losing his late father, Steve Irwin . With that, he wanted to show his mother the gratitude he feels for her.

Terri joined Robert on the dance floor toward the end of his routine … as he spun her around before breaking down in her arms.

The judges -- who were also in tears -- went on to give Robert a rave review for his per

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