The City winger scored England’s fifth goal having assisted Ross Barkley and Harry Kane as Gareth Southgate’s young side again impressed.
Sterling has – technically – now scored four and assisted three goals in the past four days for his country, taking his total for the campaign for City and England to 25.
England had gone behind after just 17 minutes but responded before the break with goals from Michael Keane and Barkley.
Barkley added a third after persistent work by Sterling and the City winger then broke clear and teed up Kane for a tap-in to seal three crucial European Championship points.
And Liverpool’s Jordan Henderson played a fine through pass for Sterling to score his fourth England goal on two games on 81 minutes as he raced clear before finishing with a clinical low drive.
Kyle Walker played another solid, dependable 90 minutes, too.
England now comfortably top their group with maximum points from two games and a healthy goal difference.
Elsewhere, Bernardo Silva played the full 90 minutes as Portugal drew 1-1 with Serbia.
Oleksandr Zinchenko was instrumental in Ukraine’s narrow 2-1 win over Luxembourg.
The City left-back assisted the opening goal with a fine through-ball and also played the full 90 minutes.
Finally, Aro Muric played a solid match for Kosovo as they held Bulgaria 1-1.