The Terriers, in the FA Cup fourth round for only the second time in 11 years, scored twice early on but had to endure a tense finale to the game as Dover turned the screw.
With the draw seeing them paired with the winner of the Arsenal v Leeds replay, the victory promises to be a very valuable one for Town.
But they had Smithies to thank when he first parried a powerful drive from Dover's 29-goal top scorer Adam Birchall on 86 minutes.
The academy product then tipped away a Harry Barker drive three minutes later, despite being wrong-footed by a deflection off Antony Kay's trailing leg.
Smithies, reputedly wanted by Aston Villa among others, deserves credit for staying alert as he had not had much to do until Dover's late revival.
Manager Lee Clark claims Smithies is not for sale and the 20-year-old added of the transfer gossip: "The manager has answered that question.
"I don't listen to rumours. That's not for me to deal with. I just get on with my job and want to concentrate on doing my best for the team."
Smithies said of his great stops: "Sometimes in football you can go for a whole game without much to do and then have to make a few saves in the 90th minute.
"Goalkeeping is all about concentration. I've learned that the best goalkeepers are concentrating all the time and are ready to make a save at any moment.
"That's what I try to do and I'm glad that I was able to make a couple of saves as it made me feel part of the win. It's fantastic to be in the fourth round."
Huddersfield went 2-0 up inside eight minutes thanks to Lee Novak setting up Scott Arfield for a tap in and then Gary Roberts in the space of 66 seconds.
Blue Square South high-fliers Dover nearly pulled one back before half-time when Roberts cleared a goal-bound Olly Schulz header off the line.
Both sides had chances after the break. Roberts and Kevin Kilbane went close for Town while the visitors were only denied by heroics from Smithies.
Huddersfield Town: Smithies; Peltier, Kay, P Clarke, Ridehalgh; Pilkington, Arfield (T Clarke 68), Kilbane, Roberts (Carey 73); Rhodes (Lee 59), Novak. Unused substitutes: Bennett, McCombe, Gudjonsson.
Dover Athletic: Flitney; Fish, Schulz, Gillman, Wynter, Baker; I'Anson, Cutler (Wallis 78), Cogan (Long 68); Hunt, Birchall. Unused substitutes: Hill, Briand, Reggett, Hook, Humphrey.
Referee: A Bates (Staffs).
Town man of the match: Peter Clarke.
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