Sterling headed home in the first half of the Three Lions' final group game to move Gareth Southgate's side above its opponent and set up a showdown with France, Germany, Portugal or Hungary next Wednesday (AEST).
The Czech Republic had their chances and must wait to discover their next opponents after slipping to third as a result of Croatia's 3-1 win over Scotland.
Jack Grealish and Bukayo Saka impressed as they came into the side along with Harry Maguire, who played 90 minutes on his return from an ankle injury for an England side that have not conceded a goal in the tournament.
The Three Lions started with great intensity and they were almost in front when Sterling lobbed Tomas Vaclik but struck the far post after he was picked out by a clever pass from Luke Shaw.
Sterling did not have long to wait for the opening goal, though, nodding home from close range 12 minutes in when the influential Grealish stood up a delightful cross from the left to the back post in a move that started with an incisive run from Saka.
Vaclik denied Harry Kane with a reflex save following a brilliant pass from Maguire, but the Czech Republic also had their chances in an entertaining first half.
Tomas Holes forced a fine reflex save from Jordan Pickford with a powerful strike and Tomas Soucek flashed a shot just wide, before Kane called Vaclik into action once again.
Both sides made a change at the break, Jordan Henderson replacing Declan Rise and Petr Sevcik on for Jakub Jankto.
The Czech Republic suffered a blow when Jan Boril was booked for a foul on the lively Saka, ruling him out of his side's last-16 tie.
Henderson had a late goal disallowed, but England responded to a lacklustre display in a goalless draw with Scotland with a second 1-0 win of the tournament.