Chris Agutter's side will visit Maidenhead United after winning 1-0 at National League South side Chippenham Town on Saturday.
The clash with the Magpies will be the fifth consecutive away tie for Hastings United in this season's FA Cup.
The winners of the third qualifying round clash between Sussex rivals Horsham and Eastbourne Borough will also take on National League opposition in Woking.
The Hornets and the Sports will do battle again on Tuesday evening after drawing 2-2 at The Camping World Community Stadium on Saturday.
Fourth qualifying round ties are scheduled for Saturday, October 16. Winners of fourth qualifying round ties will receive £9,375, while losers will get £3,125.