Hill set a record for female artists with five Grammys for her solo debut, The Miseducation of Lauryn Hill, including album of the year and best new artist.
"It's a huge thing for hip-hop music. It has to continue to stay strong and evolve because it has been music that spoke for ghetto people and for the kids. I have no fear, we will keep moving," said Hill, 23, a former member of the Fugees.
It was the first time a rap artist had ever won in those major Grammy categories.
Madonna, at age 40, won the first musical Grammys of her career for best dance recording and pop album for Ray of Light. The title song also won in the short-form music video category. Her only previous Grammy was for video in 1991.
"I have been in the music business 16 years. This is my first Grammy. Well, actually I have won four tonight. You know, it was worth the wait and all that," said Madonna, who opened the CBS-TV telecast with a Japanese-themed performance of Nothing Really Matters.
My Heart Will Go On, the ballad from Titanic, won four awards, including song and record of the year. It also won the female pop vocal award for Celine Dion, and the award for best song written for motion picture or television. James Horner and Will Jennings received the writing trophies.
Shania Twain, Stevie Wonder, the Dixie Chicks and the Brian Setzer Orchestra were double Grammy winners.
You're Still the One won best country song for Twain and husband Robert John "Mutt" Lange, and female country vocal performance for Twain.
"You never know if you're going to win. I'm happy I did," Twain said.
Probably the oldest and funniest winners are Carl Reiner and Mel Brooks who won for best spoken comedy album and got the first standing ovation of the night.
"We got a standing ovation because I said, I smell smoke," Brooks joked. "That was it. Everybody got up."
The male R&B vocal Grammy went to Wonder for St. Louis Blues. The tune also earned him and two colleagues the award for instrumental arrangement with vocals. The two Grammys brought Wonder's career total to 21.
That puts him in a tie with Pierre Boulez, who also won two awards Wednesday night, for orchestral performance and opera recording. Only Sir Georg Solti, Quincy Jones and Vladimir Horowitz have won more.