The Rams travel to five leagues higher Eastleigh aiming to pull off what would be a Hampshire Senior Cup sensation.
The Spitfires fielded a handful of first team squad players in their 3-0 second round win over Fleet Spurs.
Among them were leading scorer Scott Rendell, Sam Smart and midfielder Tom Bearwish.
All three of those players scored in the 6-1 FA Trophy thrashing of Yate at the weekend.
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Smart has so far made 18 National League appearances in his first season in the fifth tier after joining Eastleigh from Basingstoke in the summer. He was previously with Wessex Leaguers Horndean.
The winners of the Silverlake Stadium clash will join Moneyfields, Bashley and Andover New Street in the quarter finals.
Farnborough take on AFC Bournemouth on Tuesday, while the remaining three third round ties are Gosport Borough v Hawks (January 7), AFC Stoneham v Sholing (TBC) and AFC Totton v Southampton (TBC).
Hawks are aiming to win the trophy for the third year running and for the fourth time in five seasons.
Last season they made hard work of beating two divisions lower Basingstoke Town 2-1 in the final.
After Josh Huggins’ opener had been cancelled out by Ben Wright, sub Alfie Rutherford struck the winner six minutes from time.
The previous season, 2017/18, Hawks had beaten Blackfield & Langley 3-0 in the final with goals from Andreas Robinson, James Hayter and Jason Prior.