The Tottenham midfielder, who is on a season-long loan with Swansea, scored soon after the break in Prague, capitalising on a goalkeeping mistake.
Watford's Matej Vydra went closest for the hosts in the first half when his shot was cleared off the line.
The U21 European Championships will be held in Czech Republic in the summer.
England lost 3-2 in France in their last match in November, after they had won their previous 11 games, but they returned to the winner's circle after a gritty display at the Letna Stadium.
In the 12th minute, Alex Pritchard picked out Cauley Woodrow, who turned and shot just over the bar as England began brightly.
However, the Czechs were more dangerous in the rest of first half and Carroll cleared a Matej Vydra shot from a corner off the line shortly before the half-hour.
Three minutes into the second half Gareth Southgate's side edged ahead thanks to an opportunistic goal from the impressive Carroll.
Nathan Redmond did superbly to nip between two players in midfield before he spread the play out to Chambers.
The Arsenal defender's cross was fumbled by Czech goalkeeper Jiri Pavlenka and back out into the area, where Carroll arrived to stroke the ball home.
Carroll, who captained the side, was withdrawn later in the half after he picked up a knock and was replaced by Derby's Will Hughes.
But England's players finished the game strongly and apart from Ondrej Petrak's shot, which flashed past the post, England goalkeeper Marcus Bettinelli remained largely untroubled.
Match ends, Czech Republic U21 0, England U21 1.
Second Half ends, Czech Republic U21 0, England U21 1.
Attempt missed. Jiri Skalak (Czech Republic U21) right footed shot from outside the box is too high from a direct free kick.
Danny Ings (England U21) is shown the yellow card for a bad foul.
Foul by Danny Ings (England U21).
David Houska (Czech Republic U21) wins a free kick in the attacking half.
Corner,  Czech Republic U21. Conceded by Luke Garbutt.
Attempt blocked. Jiri Skalak (Czech Republic U21) right footed shot from the centre of the box is blocked. Assisted by Tomas Prikryl.
Foul by Luke Garbutt (England U21).
Ladislav Takács (Czech Republic U21) wins a free kick on the right wing.
Offside, Czech Republic U21. Tomas Kalas tries a through ball, but Jiri Skalak is caught offside.
Luke Garbutt (England U21) wins a free kick in the defensive half.
Foul by Lukas Masopust (Czech Republic U21).
Foul by John Stones (England U21).
Ladislav Takács (Czech Republic U21) wins a free kick in the defensive half.
Corner,  England U21. Conceded by Jiri Pavlenka.
Attempt saved. John Stones (England U21) header from the centre of the box is saved in the top centre of the goal. Assisted by James Ward-Prowse with a cross.
Corner,  England U21. Conceded by Tomás Holes.
Attempt blocked. Jesse Lingard (England U21) right footed shot from the centre of the box is blocked. Assisted by Nathan Redmond.
Substitution, Czech Republic U21. David Houska replaces Michal Travnik.
Offside, England U21. Will Hughes tries a through ball, but Danny Ings is caught offside.
Foul by John Stones (England U21).
Ladislav Takács (Czech Republic U21) wins a free kick on the left wing.
Foul by Danny Ings (England U21).
Tomas Kalas (Czech Republic U21) wins a free kick in the defensive half.
Foul by Danny Ings (England U21).
Patrizio Stronati (Czech Republic U21) wins a free kick in the defensive half.
Carl Jenkinson (England U21) wins a free kick in the defensive half.
Foul by Ladislav Takács (Czech Republic U21).
Carl Jenkinson (England U21) wins a free kick in the defensive half.
Foul by Lukas Masopust (Czech Republic U21).
Hand ball by Jiri Skalak (Czech Republic U21).
Substitution, Czech Republic U21. Tomas Prikryl replaces Matej Vydra.
Substitution, Czech Republic U21. Ladislav Takács replaces Ondrej Petrak.
Substitution, England U21. John Stones replaces Liam Moore.
Attempt missed. Jiri Skalak (Czech Republic U21) right footed shot from outside the box is too high. Assisted by Lukas Masopust following a fast break.
Corner,  England U21. Conceded by Patrizio Stronati.
Attempt missed. Jaromir Zmrhal (Czech Republic U21) right footed shot from outside the box misses to the left. Assisted by Tomás Holes.
Corner,  England U21. Conceded by Jiri Pavlenka.
Substitution, England U21. Danny Ings replaces Cauley Woodrow.
Tom Carroll's second-half strike gave England Under-21s a 1-0 win in the Czech Republic - and a 12th win in 13 games for Gareth Southgate's side.