The 19-year-old striker – on-loan from Aston Villa – struck a hat-trick as the League One high-flyers triumphed 3-0 at the home of The Hawks.
After netting twice in the first half, Robinson ensured he would be taking home the match ball as he converted a late penalty.
Havant & Waterlooville 0-3 Preston
The FA Cup First Round Proper
Monday 10 November
Martin Road, Havant
If the scoreline was not devastating enough, things were made worse for the Conference South side as they were forced to finish the match with only nine men.
Midfielder Brian Stock was shown his second yellow card of the evening on 59 minutes before Warren Cummings was given his marching orders after handling in the area with ten minutes to go – giving Robinson the opportunity to seal his treble.
Preston will host either Walsall or Shrewsbury Town in The FA Cup Second Round.
A jubilant Robinson said afterwards: "It's a big thing for me to play my first game in the FA Cup and get a hat-trick. I am learning each day here and hopefully I can go back to Villa with some more experience."
Manager Simon Grayson said: "We are grateful to Aston Villa for letting him come out on loan. He's a young kid learning the game and this will have been a great experience for him. He only got his first league goal recently and now he has an FA Cup hat-trick to his name.
"He has a fantastic attitude, wants to work hard, has quick feet, awareness and once he gets defenders on the back foot he can finish too.
"We needed an early goal to settle us and the players knew they had to be professional to get through. Callum's second goal would not have looked out of place in the Premier League. He only got his first league goal recently and now he has an FA Cup hat-trick to his name."
Havant & Waterlooville manager Lee Bradbury conceded: "The first red card counted against us when we were already down against a good team.
"But I've reminded the players we have been beaten by a very good side and this was a bonus for the lads tonight. We can move forward from here. The lads showed they can play a bit of football and things just didn't go for us."
