The Terriers, who lost their previous two away games, hit the post through Elias Kachunga in the first half.
Schindler's downward header from Aaron Mooy's corner gave the visitors the lead after the break.
Ipswich's Grant Ward volleyed wide from a Leon Best flick-on but they have now won just two of their past 11 games.
Tom Lawrence sent a free-kick just wide for the hosts in the first half, but Mick McCarthy's side lacked a cutting edge in the final third.
Listen to Huddersfield boss David Wagner speaking to BBC Radio Leeds
They have failed to score in their past four Championship games and have scored just four goals in their past 10 league games since hitting four past Barnsley on the opening day.
Huddersfield's attacks mostly came on the counter and they were content to defend their lead in the second half, but Kachunga was very unlucky not to have opened the scoring earlier when his sweet strike struck the post.
The Terriers have won eight of their first 11 league games and are now 12 points ahead of McCarthy's Ipswich.
Huddersfield Town manager David Wagner:
"I am very surprised as the only teams who could have expected this start is Newcastle, Norwich and Aston Villa.
"But I am not surprised by how my players are working together and how fit they are. In football, it is all about the little details and getting these details right to win games.
"For any manager in the Championship, three points at Ipswich is huge. This is a very difficult place to come against an aggressive team but we stayed in the game and then got our goal."
Ipswich Town manager Mick McCarthy:
"We weren't very good on the ball and we didn't create anything. We have got some injuries but I expect more from the players I had out on the pitch.
"It is difficult at the moment. I am not surprised by the fans' reaction. We did not play as well as we could and the crowd are getting frustrated and venting their feelings.
"I am doing the job to the best of my ability but if we are not as good as the crowd think we should be, then they pay their money and it is up to them if they want to boo. I am not happy with how we played myself."
Match ends, Ipswich Town 0, Huddersfield Town 1.
Second Half ends, Ipswich Town 0, Huddersfield Town 1.
Attempt missed. Christophe Berra (Ipswich Town) header from the right side of the six yard box is just a bit too high. Assisted by Teddy Bishop with a cross following a corner.
Corner,  Ipswich Town. Conceded by Danny Ward.
Corner,  Ipswich Town. Conceded by Mark Hudson.
Nahki Wells (Huddersfield Town) wins a free kick in the defensive half.
Foul by Cole Skuse (Ipswich Town).
Attempt missed. Luke Varney (Ipswich Town) right footed shot from outside the box is high and wide to the right.
Attempt blocked. Christophe Berra (Ipswich Town) right footed shot from the centre of the box is blocked. Assisted by Luke Varney with a headed pass.
Nahki Wells (Huddersfield Town) wins a free kick in the defensive half.
Foul by Cole Skuse (Ipswich Town).
Substitution, Huddersfield Town. Martin Cranie replaces Sean Scannell.
Attempt missed. Michael Hefele (Huddersfield Town) header from the centre of the box is high and wide to the left. Assisted by Aaron Mooy with a cross following a set piece situation.
Substitution, Ipswich Town. Luke Varney replaces Tom Lawrence.
Elias Kachunga (Huddersfield Town) wins a free kick on the right wing.
Foul by Christophe Berra (Ipswich Town).
Attempt missed. Teddy Bishop (Ipswich Town) right footed shot from the centre of the box is close, but misses to the left.
Foul by Nahki Wells (Huddersfield Town).
Christophe Berra (Ipswich Town) wins a free kick in the defensive half.
Rajiv van La Parra (Huddersfield Town) wins a free kick in the defensive half.
Foul by Joshua Emmanuel (Ipswich Town).
Sean Scannell (Huddersfield Town) wins a free kick in the defensive half.
Foul by Teddy Bishop (Ipswich Town).
Offside, Ipswich Town. Jonas Knudsen tries a through ball, but Leon Best is caught offside.
Delay over. They are ready to continue.
Delay in match Nahki Wells (Huddersfield Town) because of an injury.
Substitution, Huddersfield Town. Michael Hefele replaces Christopher Schindler because of an injury.
Delay over. They are ready to continue.
Delay in match Leon Best (Ipswich Town) because of an injury.
Delay over. They are ready to continue.
Delay in match Christopher Schindler (Huddersfield Town) because of an injury.
Attempt saved. Freddie Sears (Ipswich Town) right footed shot from outside the box is saved in the top centre of the goal. Assisted by Tom Lawrence.
Attempt blocked. Rajiv van La Parra (Huddersfield Town) right footed shot from outside the box is blocked. Assisted by Aaron Mooy.
Attempt blocked. Sean Scannell (Huddersfield Town) left footed shot from the centre of the box is blocked. Assisted by Elias Kachunga.
Attempt blocked. Nahki Wells (Huddersfield Town) right footed shot from outside the box is blocked. Assisted by Aaron Mooy.
Mark Hudson (Huddersfield Town) wins a free kick in the defensive half.
Foul by Christophe Berra (Ipswich Town).
Goal!  Ipswich Town 0, Huddersfield Town 1. Christopher Schindler (Huddersfield Town) header from the left side of the six yard box to the bottom right corner. Assisted by Aaron Mooy with a cross following a corner.
Corner,  Huddersfield Town. Conceded by Luke Chambers.
Offside, Ipswich Town. Tom Lawrence tries a through ball, but Freddie Sears is caught offside.
Huddersfield extended their lead at the top of the Championship with victory in an even game at Ipswich thanks to Christopher Schindler's header.