The service, held at St. Bartholomew's Church in Manhattan, New York City, included words of tribute from Sir Mick as well as Ms Scott's brother, Randy Bambrough; her good friend actress Ellen Barkin; fashion personality Andre Leon Talley and actress Sarah Jessica Parker.
Poems were shared by Ms Scott's niece, Hannah Bambrough, and Sir Mick's son, James Jagger. The Rolling Stones rocker's grandchildren, Mazie and Zak, read Psalm 23.
Besides Sir Mick's rendition of the Dylan song, his backup singer Lisa Fischer sang Amazing Grace.
The service was followed by a reception.
Others attending included actresses Julianne Moore, Meg Ryan, Olivia Munn and Renee Zellweger; Vogue editor Anna Wintour; film directors Martin Scorsese and Baz Luhrmann; and Vanity Fair editor Graydon Carter. Fans lined against barricades to take photos.
A small private funeral was held for Ms Scott in Los Angeles in March.