The Actual Battle
Grant used stealth and deception to slip away from the lines around Cold Harbor and shift his army south of the James river. By the morning of June 15, he was ready to launch his attack. Grant Smith delayed his assault until 7:00 pm to expect the momentary arrival of General Winfield S. Hancock. With daylight fading away Smith ordered his army to attack and causing some of the confederate army to panic and surrender, but darkness had become a fact now. Grant and Hancock agreed to postpone any further offensive action until dawn. This decision destroyed their chance of capturing Petersburg over night.
http://www.civilwar.org/battlefields/petersburg.html?tab=facts
http://www.civilwar.org/battlefields/petersburg.html?tab=facts
The Result of the Battle
Since the two generals, Smith and Hancock, had missed their chance of taking Petersburg by waiting overnight. Therefore letting the rebels fortify their defensive position to the east. The next morning the Union solders couldn't break their defense and the American flag didn't fly over Petersburg for another 291 days.
http://www.civilwar.org/battlefields/petersburg.html?tab=facts
http://www.civilwar.org/battlefields/petersburg.html?tab=facts