I Advise That All Preparations Be Made For Leaving Richmond Tonight

The Appomattox Campaign

Grant's general offensive along the Petersburg siege lines began at 430am on Sunday morning April 2, 1865.  Fierce fighting erupted on the entire front.  Though some Confederate troops fought tenaciously (see, for instance the defense of Fort Gregg, called by some "The Confederate Alamo", the Union forces began to break through.
(Storming Fort Gregg from petersburgsiege.org)

At 1040am Confederate Secretary of War John Breckinridge (a former United States Senator, Vice-President of the United States under President Buchanan (1857-61) and one of three rivals to Abraham Lincoln in the presidential election of 1860) received a telegram from Robert E Lee:
(Breckinridge)

I see no prospect of doing more than holding our position here until night.  I am not certain I can do that.  If I can I shall withdraw to-night north of the Appomattox, and, if possible, it will be better to withdraw the whole line to-night from the James River.  I advise that all preparations be made for leaving Richmond tonight.

President Jefferson Davis received Lee's message while attending Sunday services at St Paul's Episcopal Church in Richmond.
 
Late that day, Lee told the War Department "It is absolutely necessary that we abandon our position tonight, or run the risk of being cut off in the morning".

At 8pm, Confederate troops began evacuating Petersburg and Richmond.

By 11pm, Jefferson Davis and the Confederate Cabinet departed Richmond by train from the Richmond & Danville Railroad depot (the same railroad mentioned in The Band's 1969 song The Night They Drove Old Dixie Down, "Virgil Caine is the name, and I served on the Danville train) headed towards Lynchburg and then south hoping to join Johnston's army in North Carolina and continue the fight.