While the Confederates tried to break out of the siege Grant was away from the army discussing with the navy what the next step would be. The navy was too battered to be of much use so Grant knew he'd have to finish the job alone. Upon his return to the army that afternoon he found out the extent of the damage and that an escape route had been cleared. Grant resolved to counter attack and win back what had been lost. In many places his men were able to recapture most of the lost ground, this was also because the Confederates had decided to return to their lines, get some rest and make their escape the next morning.
On Grant's left he ordered CF Smith's division to assault the lines closest to the fort, this area had not been part of the earlier fighting. The Confederates had pulled men from this area to make the breakout attempt, so Smith's men faced a much smaller force and were able to drive the Confederates back from these outer works. In the pictures you'll see a cannon, that cannon represents Jackson's Virginia battery and it had been pulled from the line earlier.