Lee Novak rolled the hosts into the lead from the penalty spot after Lloyd Dyer upended Jack Hunt in the area.
Foxes substitute Wood calmly slotted home Ritchie De Laet's low cross to send the tie to a replay.
The result was a stark contrast to when the teams last met, on New Year's Day, when Nigel Pearson's side
cruised to a 6-1 victory.
Both sides made a number of changes, with Town making four to the team beaten 4-0 at Watford last week while the Foxes made five alterations to the XI that beat Middlesbrough 1-0 last Friday.
Hot shot Wood
Chris Wood has scored 17 goals in 23 appearances this season. He has six in his last four starts for Leicester.
Caretaker manager Mark Lillis will have been pleased with the energetic way his side started the match and they should have taken the lead when Peter Clarke met Oliver Norwood's cross but he failed to keep his header down.
Neither goalkeeper was called into action in a first half where both teams struggled to create any clear chances, Martyn Waghorn going closest for the Foxes with a low volley from 20 yards that went just wide.
The Terriers made a bright start to the second period and it took an excellent interception from Foxes skipper Wes Morgan to stop Novak opening the scoring from Hunt's cutback before James Vaughan fired an acrobatic effort straight at visiting keeper Kasper Schmeichel.
This forced the Foxes into life and strikers Wood and David Nugent came on for James Vardy and Waghorn.
New Zealand international Wood almost had an immediate impact but his curled effort from just outside the area was well saved by Terriers keeper Alex Smithies.
The game was starting to open up and Novak should have put the hosts in front but he directed his header too close to Schmeichel and the visitors managed to get the ball to safety.
Novak eventually got the better of the Leicester number one when he stroked home from the penalty spot after Dyer tripped the enterprising Hunt in the area.
The hosts had chances to wrap up the win but Vaughan poked just wide from six yards while Clarke had a header cleared off the line by Danny Drinkwater.
They were left to regret those misses when Wood showed good composure to slot home De Laet's cross after Dyer's neat dummy.
The result brought to an end Leicester's run of five successive victories while Town have now won just once in 14 games in all competitions.
Leicester City boss Nigel Pearson:
"I just look at our performance and we were disjointed, we didn't pass the ball as well as we can.
"We showed some good qualities to get back in it but a draw isn't an ideal result. Having said that I'd rather not lose a game.
"We don't have a big squad but we have a fair amount of quality in there.
"Give them credit, it was a very spirited performance. They chose to make a change during the week and it's always sad to see a manager lose his job."
Huddersfield caretaker-manager Mark Lillis:
"It was a great experience for myself. I'm proud to have led the club in an FA Cup tie and to see them play like that.
"I think they're the best team in the Championship and they showed us respect when they had to bring on their main strikers.
"I wanted to get the boys passing again and I gave Jordan Sinnott a debut and I thought he was excellent.
"I found out at 14:00 on Thursday what had happened and that I was being asked to lead the team."
On whether he wants the job: "I'm academy manager and when they appoint a new boss that is the role I will go back to. My focus has just been on today and I'll speak to the chairmen later because we have Crystal Palace here on Wednesday."
The referee blows for offside. Alex Smithies restarts play with the free kick.
Foul by Ritchie De Laet on Alan Lee, free kick awarded. Free kick crossed by Adam Clayton, clearance by Wes Morgan.
Anthony Gerrard takes a shot. Kasper Schmeichel makes a comfortable save.
Outswinging corner taken right-footed by Oliver Norwood, Ritchie De Laet makes a clearance.
Booking Ben Marshall goes into the referee's book.
Free kick awarded for a foul by Ben Marshall on Sean Scannell. Direct free kick taken by Adam Clayton.
The ball is swung over by Ben Marshall, Header from deep inside the area by Ritchie De Laet goes harmlessly over the crossbar.
Booking The referee books Adam Clayton for dissent.
James Vaughan gives away a free kick for an unfair challenge on Ben Marshall.
Assist on the goal came from Ritchie De Laet.
81:35 Goal scored
Goal! - Chris Wood - Huddersfld 1 - 1 Leicester Goal scored by Chris Wood from just inside the penalty area to the bottom left corner of the goal. Huddersfield 1-1 Leicester.
Substitution Lee Novak goes off and Alan Lee comes on.
Oliver Norwood takes the inswinging corner, Peter Clarke takes a shot. Lloyd Dyer makes a clearance.
James Vaughan produces a right-footed shot from deep inside the six-yard box which goes wide of the right-hand post.
Corner taken by Oliver Norwood.
73:16 Goal scored
Goal! - Lee Novak - Huddersfld 1 - 0 Leicester Penalty taken right-footed by Lee Novak and scored. Huddersfield 1-0 Leicester.
Jack Hunt fouled by Lloyd Dyer, the ref awards a Penalty.
Free kick awarded for a foul by Sean Scannell on Andy King. The free kick is swung in right-footed by Ben Marshall, Peter Clarke manages to make a clearance.
Booking Booking for Lee Novak.
Free kick awarded for an unfair challenge on Ritchie De Laet by Lee Novak. Ritchie De Laet takes the direct free kick.
Substitution (Leicester) makes a substitution, with Danny Drinkwater coming on for Richie Wellens.
Effort on goal by James Vaughan from inside the penalty area goes harmlessly over the bar.
Lee Novak takes a shot. Save made by Kasper Schmeichel. Corner from the right by-line taken by Oliver Norwood, Andy King makes a clearance.
Substitution Sean Scannell comes on in place of Jordan Sinnott.
Shot by Ben Marshall from outside the box goes high over the target.
Chris Wood takes a shot. Save by Alex Smithies. Corner taken by Ben Marshall from the right by-line, save by Alex Smithies.
The referee blows for offside. Alex Smithies restarts play with the free kick.
Substitution David Nugent joins the action as a substitute, replacing Jamie Vardy.
Substitution Chris Wood is brought on as a substitute for Martyn Waghorn.
Lee Novak gets a header at goal, Jamie Vardy challenges Jack Hunt unfairly and gives away a free kick. Free kick crossed right-footed by Adam Clayton from right by-line, Wes Morgan makes a clearance. Clearance made by Ben Marshall. Corner from the left by-line taken by Oliver Norwood, Effort on goal by Peter Clarke from deep inside the penalty area misses to the right of the target.
Free kick awarded for a foul by Richie Wellens on Adam Clayton. Free kick crossed right-footed by Oliver Norwood from left channel, save by Kasper Schmeichel.
Oliver Norwood takes the outswinging corner, save by Kasper Schmeichel.
The referee blows for offside. Anthony Gerrard takes the direct free kick.
Booking Booking for Oliver Norwood for unsporting behaviour.
Martyn Waghorn concedes a free kick for a foul on Peter Clarke. Free kick taken by Alex Smithies.
Jordan Sinnott takes a shot from a long way out clearing the bar.
The referee gets the second half underway.
45:00 +1:01 Half time
Half Time The referee calls an end to the first half.
James Vaughan is flagged offside by the assistant referee. Direct free kick taken by Kasper Schmeichel.
Free kick awarded for a foul by Scott Arfield on Ben Marshall. The free kick is delivered left-footed by Martyn Waghorn from right channel, clearance made by James Vaughan.
Free kick awarded for an unfair challenge on Andy King by Adam Clayton. Richie Wellens takes the direct free kick.
Lee Novak has an effort at goal from just inside the box that misses to the right of the goal.
Lee Novak is caught offside. Free kick taken by Kasper Schmeichel.
The official flags James Vaughan offside. Kasper Schmeichel restarts play with the free kick.
The free kick is delivered right-footed by Adam Clayton from left channel, clearance by Martyn Waghorn.
Booking Michael Keane goes into the referee's book.
Michael Keane gives away a free kick for an unfair challenge on James Vaughan.
Effort from just outside the area by Jack Hunt goes over the target.
Foul by Ritchie De Laet on Calum Woods, free kick awarded. Anthony Gerrard takes the free kick.
Jack Hunt challenges Lloyd Dyer unfairly and gives away a free kick. Ben Marshall shoots direct from the free kick, clearance by Andy King. Martyn Waghorn takes a inswinging corner to the near post, clearance by Adam Clayton.
Martyn Waghorn produces a right-footed shot from just outside the box that goes wide right of the goal.
Adam Clayton produces a cross.
The ball is crossed by James Vaughan.
Outswinging corner taken right-footed by Oliver Norwood from the right by-line, Shot from inside the area by Peter Clarke clears the bar.
Jamie Vardy fouled by Calum Woods, the ref awards a free kick. Richie Wellens takes the free kick.
Andy King gives away a free kick for an unfair challenge on Adam Clayton. Oliver Norwood produces a strike on goal direct from the free kick, Andy King gets a block in.
Free kick awarded for an unfair challenge on Lloyd Dyer by Jordan Sinnott. Free kick taken by Paul Konchesky.
Martyn Waghorn is flagged offside by the assistant referee. Peter Clarke takes the direct free kick.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.