Thomas Tuchel’s side dominated from kick-off, with Anderson the orchestrator for a handful of England chances.
This also saw Anderson pressed often, with Pavel Sulc shown a straight red card on 25 minutes for a high tackle on the City midfielder.
Despite facing 10 men, England had to be patient and it wouldn’t be until the 47th minute when Anthony Gordon headed in Trent Alexander-Arnold’s deep cross.
The visitors finally provided themselves with a bit of breathing room when Harry Kane fired home a loose ball from close range with the Czech Republic struggling to go man for man.
The win in Prague means England sit second with three points after two games played.
In the other League A Group 3 fixture, Mateo Kovačić and Joško Gvardiol started in Croatia’s 4-1 loss to World Cup champions Spain.
Lamine Yamal needed just two minutes to put the hosts ahead. Dion Beljo levelled the score just before the half hour, but Marc Pubill quickly restored Spain’s lead.
A second of the evening for Yamal before a late goal for substitute Nico Williams put the game of reach for Croatia.
They will be looking to return to winning ways when they host England on Saturday 3 October, with kick-off set for 17:00 (UK).
Earlier in the day, Vitor Reis was an 87th-minute substitute in Brazil’s 4-2 win over Australia for his second cap for his nation’s senior team.
And Ryan McAidoo helped England’s Under-19s beat Norway 2-1 in a friendly camp in Spain.
