The Manchester City winger headed home Jack Grealish’s pinpoint cross from close range in the 12th minute to settle a tight contest with his second goal of the tournament.
John Stones and Kyle Walker both started alongside Sterling at Wembley Stadium, but Phil Foden was left out of the squad to avoid picking up a booking that would have meant he missed the first game of the knockout stage.
England will face France, Germany, Portugal or Hungary at Wembley in the last 16, with this victory meaning they progress with an unbeaten record.
Gareth Southgate’s side might have enjoyed a more comfortable victory against the Czechs, with Jordan Henderson having a late strike ruled out for offside, whilst Sterling, who was substituted in the 66th minute, saw a second minute chip bounce agonisingly back off the post after he latched onto Luke Shaw’s forward ball.
The Three Lions were looking for a response after the frustrating stalemate against Scotland and they started brightly at Wembley.
The goal, headed in from six yards after Grealish combined with Harry Kane following a brilliant run from Bukayo Saka, was no more than they deserved and Kane came close to doubling the lead, only to be denied by Tomas Vaclik's strong hand.
However, the opposition still had their moments.
Tomas Soucek fired just wide after Shaw’s clearance dropped invitingly for him inside the area and Tomas Holes forced a good save from Jordan Pickford with a well-stuck 20-yard drive before the game petered out in a low-key second half.
Elsewhere in Group D, Scotland’s tournament came to an end after they fell to a 3-1 defeat against Croatia.