The National League South Stones - thrust into focus after stunning League One Stevenage on Saturday - will travel to Championship promotion-chasers Ipswich Town.
Eastleigh, who have to get past Newport County in a replay next week, will host Wigan or Manchester United if they can get the job done.
Third round winners earned a fee of £105,000 while those who progress into the fifth round will score a whopping £120,000 pay cheque.
The fourth round ties will take place on the weekend of January 27 and 28. The live game will be announced in the days ahead.