Gareth Southgate's side just about edged the first half before shifting up a couple of gears after half-time.
Sterling's superb tournament continued as England went ahead on four minutes.
The City forward slid a peach of pass into the path of Harry Kane who prodded past the keeper from close range to get England off to a flying start in Rome.
It was a pass of a player brimming with confidence as the Three Lions' momentum and belief continues to grow.
Up to that stage, Andriy Shevchenko's men were very much in the game, but within five minutes of the restart, England had blown them away with further goals from Harry Maguire and another for skipper Kane - both supplied by United's Luke Shaw - making it 3-0.
Sterling played a neat pass to Shaw in the build-up to the third.
Sub Jordan Henderson nodded in a fourth just after the hour-mark as a tiring Ukraine struggled to cope with the waves of English attacks.
Stones and Walker had little to do in the second-half, but both completed 90 minutes as England set a new European Championships record of five clean sheets in the opening five games.
Denmark now await in the semi-final at Wembley next Wednesday with the chance of a first final in the competition for the Three Lions tantalisingly close.