Callum Cooke scored his first goal for the club to give Hartlepool the lead before Josh Umerah added to their lead from the penalty spot in first half stoppage time.
Umerah was brought down by Joe Mattock who was shown a second yellow card for the challenge and sent off as Pools doubled their lead.
And Umerah grabbed his second of the game in the second half when powering home from Joe Grey’s clever through ball to put the tie beyond doubt.
Harrogate did manage to score a consolation through Josh Coley to deny debut goalkeeper Alex Cairns, an emergency loan signing from Fleetwood Town, a clean sheet but it will be Hartlepool involved in the third round draw.
And here is how Pools were rated in their FA Cup success:
1. Alex Cairns - 7
Brought in as an emergency loan option after injuries to Ben Killip and Kyle Letheren and was largely untroubled. Looked assured. Made a decent low save from Falkingham. Beaten well by Coley. (Credit: Mark Fletcher | MI News) Photo: Mark Fletcher
2. Reghan Tumilty - 7
Looked solid defensively against some potentially tricky opponents in Muldoon, Grant and Pattison and got forward well again. Had to move out to the left second half and was comfortable. (Credit: Mark Fletcher | MI News) Photo: Mark Fletcher
3. Rollin Menayese - 8
Much welcome return. Brought a calmness to the defence. Dealt with Armstrong well and provided pace when needed. Strong performance. (Credit: Mark Fletcher | MI News) Photo: Mark Fletcher
4. David Ferguson - 7
Credit to him. Good display at centre-back considering he was taken off with what looked a difficult injury a week ago. Took a whack in the first half from Armstrong but kept things simple and did what he needed to do. Covered Oduor well when he went forward. (Credit: Michael Driver | MI News) Photo: Michael Driver