Pools overcame Exeter City 1-0 - completing an incredible comeback after being 2-0 down in the original tie.
Josh Hawkes’ goal in extra time set up a January game at League One Oxford United. There was no joy for Eastleigh, they went down 3-1 at Crewe.
Yeovil Town moved into second with another win but Chesterfield still can’t get themselves going.
The Glovers’ secured back-to-back wins with victory at the ProAct - a result which takes them to within three points of leaders Barrow.
First half goals from Myles Hippolyte and Rhys Murphy, who won and scored his penalty, kept Chesterfield second from bottom.
Sutton’s improvement continues after holding firm at AFC Fylde.
The game finished goalless at Mill Farm with neither side able to convert their chances.
In the National League South, Wealdstone moved seven points clear after a professional 2-0 win over Eastbourne Borough.
Dennon Lewis got them going with little over a quarter of an hour played. Captain Jerome Okimo doubled the lead before the break and that’s how it stayed.
Neither side could break through at the Gallagher Stadium as Maidstone United and Chippenham played out a goalless draw.
There was only one game in the North, managerless Kidderminster Harriers running out 2-1 winners at Guiseley. Sam Austin netted the winner.
National League results:
AFC Fylde 0-0 Sutton United
Chesterfield 1-2 Yeovil Town
FA Cup second round replays:
Hartlepool United 1-0 Exeter AET
Crewe 3-1 Eastleigh
National League South results:
Maidstone United 0-0 Chippenham
Wealdstone 2-0 Eastbourne
National League North result:
Guiseley 1-2 Kidderminster H