After jet setting across the US, Rihanna managed to discreetly visit six-year-old leukemia patient Jasmina Anema, one of her biggest fans. The singer made a trip into her hospital room at NYU Medical Center on April 2.

"She's really here!" Jasmina exclaimed when Rihanna came in, shoeless, to prevent the spread of germs, and hugged her. "You are such a beautiful little girl," the singer told Jasmina, who has a rare and aggressive form of leukemia.

High doses of chemotherapy often leave Jasmina tired, says Katharina Harf, executive vice president of DKMS Americas, the bone marrow donor registry that is helping Jasmina and others find a match. "But when Rihanna walked into the room, there was no sign of that at all," she says. "Jasmina loves Rihanna. And Rihanna fell in love with Jasmina."

The two spent more than three hours talking, playing and indulging in a slumber party-like pillow fight. They even danced to Rihanna's biggest hits including "Umbrella" and "Please Don't Stop the Music." "Jasmina showed Rihanna all her special 'moves' and tried to teach her how to do them," says Harf.

Rihanna first learned about Jasmina's plight in early February, when she saw the moving video Jasmina's best friend, Isabelle Huurman, and her mother, Karen Detrick, made appealing for donors to save Jasmina. Wanting to help her however she could, Rihanna put a shout out for donors on Feb. 7 on PEOPLE.com to help Jasmina find a match, which drew more than 4,000 donors.

The visit was supposed to last for about an hour. "But Rihanna stayed until 8 o'clock that night," says Harf. "She would have stayed longer if Jasmina didn't have to go to sleep."

The visit was a total pinch-me moment for Jasmina, who at one point pointed to the picture of Rihanna on her CD cover, and with big eyes, whispered, "‘Look! It's her! Really her!!'" says Harf.

Jasmina, who is a "total girly girl," according to her mother, Thea Anema, was thrilled when Rihanna presented her with a big bag of Cover Girl makeup. "Rihanna asked me if it was okay to put makeup on Jasmina," says Anema. "I said, 'Of course!' She's so thrilled with makeup and anything girly."

Rihanna painted the little girl's nails and gently brushed "Dance Party" eyeshadow on her tiny eyelids. They played catch together with Jasmina's stuffed dog, Jackie, which ended with a torrent of giggles and hugs. "Rihanna kept on saying, 'I love her personality! She is such a little diva!' " says Harf. When Rihanna learned that Jasmina speaks Dutch and also understands Mandarin, the superstar said she was amazed at how "intelligent" and "what an amazing little girl" she is.

Jasmina's mom stood teary-eyed as she watched her daughter laugh and play with Rihanna. "You have no idea how much this means to her," she told Rihanna. "It was like they had known each other forever. Rihanna is a beautiful girl."

Adds Harf: "If we could have done anything to make Jasmina happy, this was it. And Rihanna was just as happy. Rihanna has such a big heart. She loves children so much – and it showed."

The visit with Jasmina meant a lot to Rihanna, too. "It breaks my heart to see her go through this difficult sickness," Rihanna tells PEOPLE exclusively. "Jasmina still hasn't found a match and she is just one of 6,000 people suffering from leukemia or other blood cancers who search the registry every day for a life-saving match. We can take action and sign up to be bone marrow donors. We can save the life of Jasmina and others like her."

For more information, on how to become a donor, please visit www.OneForJasmina.com or DKMSAmericas.org. If you want to sign up as a bone marrow donor with DKMS, go to www.dkmsamericas.org/category/marrow-donors/become-donor.