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Daryl Murphy put the visitors ahead early on with his first goal for the club - and only the second by the Magpies in their past six FA Cup ties.
They had Aleksandar Mitrovic carried off before Jutkiewicz turned in Jonathan Grounds' low cross to level.
But he twice missed late chances to steal victory for the hosts.
Both sides rang the changes with Newcastle making eight to Birmingham's five, but it was the Magpies who sent their 4,671 travelling fans into raptures, in an all-Championship meeting of 13th against second, when Murphy scored from close range five minutes into his second start for Rafael Benitez's side.
However, it came at a cost as fellow striker Mitrovic suffered a badly cut leg in the build-up.
The visitors had chances to extend their lead, with sub Yoan Gouffran firing wide before Grant Hanley headed just over.
Che Adams went close with a long-range shot for Blues prior to Jutkiewicz's equaliser and Grounds could have put the home side in front by the break, with his fierce half-volley flying just over.
Blues are yet to win in five matches under Zola, but it was the Italian's side that came closest to a winner against his Spanish counterpart Benitez, who lifted the FA Cup with Liverpool in 2006.
Although Matt Ritchie made an impact for Newcastle off the bench, it was Jutkiewicz who should have won it, steering a free header wide from a cross by Josh Dacres-Cogley from six yards, before then going close again.
Birmingham were beaten 4-0 at St James' Park in December, but when they played there in an FA Cup third-round replay 10 years ago, they won 5-1.
Birmingham boss Gianfranco Zola told BBC WM: "We had good chances to win it. But Lukas does not need to apologise. Next time they will go in.
"It was important that we got something out of it. It will give big belief to the players. It is the best we have played in terms of consistency.
"You could see at the beginning. We were a bit edgy and there were nerves on the bench too, but I am now more optimistic. The players are now starting to understand more what we are trying to do.
"A win would be massive. You can do good things on the pitch but you need to win. Without confidence, you can't do anything."
Newcastle manager Rafael Benitez told BBC Sport: "A replay is not ideal, for them or us. We made a lot of changes and changed the system but we had started well and had control before the injury to Mitrovic.
"Daryl Murphy put in a tremendous effort. I'm really pleased with him and the fact that he scored too. He's a great professional.
"I always approach every game looking to win. For me, the FA Cup is a massive competition. I won it with Liverpool in 2006 and I will try to do it with this squad too."
Match ends, Birmingham City 1, Newcastle United 1.
Second Half ends, Birmingham City 1, Newcastle United 1.
Attempt blocked. Che Adams (Birmingham City) right footed shot from outside the box is blocked. Assisted by Maikel Kieftenbeld.
Foul by David Davis (Birmingham City).
Jack Colback (Newcastle United) wins a free kick in the defensive half.
Corner,  Birmingham City. Conceded by Grant Hanley.
Greg Stewart (Birmingham City) wins a free kick in the defensive half.
Foul by Achraf Lazaar (Newcastle United).
Attempt missed. Lukas Jutkiewicz (Birmingham City) header from the centre of the box is close, but misses to the right. Assisted by David Davis with a cross.
Foul by David Davis (Birmingham City).
Grant Hanley (Newcastle United) wins a free kick in the defensive half.
Foul by Greg Stewart (Birmingham City).
Jack Colback (Newcastle United) wins a free kick in the defensive half.
Attempt missed. Lukas Jutkiewicz (Birmingham City) header from the centre of the box misses to the left. Assisted by Josh Cogley with a cross.
Substitution, Birmingham City. Greg Stewart replaces Diego Fabbrini.
Foul by Josh Cogley (Birmingham City).
Matt Ritchie (Newcastle United) wins a free kick on the left wing.
Paul Robinson (Birmingham City) wins a free kick in the defensive half.
Foul by Matt Ritchie (Newcastle United).
Offside, Newcastle United. Daryl Murphy tries a through ball, but Matt Ritchie is caught offside.
Substitution, Newcastle United. Matt Ritchie replaces Massadio Haidara.
Corner,  Newcastle United. Conceded by Ryan Shotton.
Isaac Hayden (Newcastle United) is shown the yellow card for a bad foul.
Attempt saved. David Davis (Birmingham City) left footed shot from outside the box is saved in the centre of the goal. Assisted by Che Adams.
Substitution, Newcastle United. Isaac Hayden replaces Cheick Tioté.
Stephen Gleeson (Birmingham City) wins a free kick in the attacking half.
Foul by Jack Colback (Newcastle United).
David Davis (Birmingham City) wins a free kick in the attacking half.
Foul by Cheick Tioté (Newcastle United).
Lukas Jutkiewicz (Birmingham City) wins a free kick on the left wing.
Foul by Jamaal Lascelles (Newcastle United).
Foul by Lukas Jutkiewicz (Birmingham City).
Grant Hanley (Newcastle United) wins a free kick in the defensive half.
Foul by Lukas Jutkiewicz (Birmingham City).
Cheick Tioté (Newcastle United) wins a free kick in the defensive half.
Attempt missed. Diego Fabbrini (Birmingham City) left footed shot from outside the box is close, but misses to the right. Assisted by Stephen Gleeson with a headed pass.
Second Half begins Birmingham City 1, Newcastle United 1.
First Half ends, Birmingham City 1, Newcastle United 1.
Ryan Shotton (Birmingham City) wins a free kick in the defensive half.
Foul by Grant Hanley (Newcastle United).
Lukas Jutkiewicz kept Gianfranco Zola's Birmingham City in the FA Cup as they came from behind to earn a third-round replay against Newcastle.