The winger, who completed an hour of the Three Lions’ triumph, raced past Egidijus Vaitkūnas before pulling back for captain Jermain Defoe to convert from close range.
Sterling was brought off on the hour-mark to be replaced by Marcus Rashford, while John Stones and Joe Hart completed the full 90 minutes.
Jamie Vardy doubled England’s lead with a 66th-minute effort.
Meanwhile, Leroy Sane was introduced for the final five minutes of Germany’s 4-1 thrashing of Azerbaijan.
Andre Schurrle’s brace, accompanied by Thomas Muller and Mario Gomez strikes handed the visitors the win.
Both group leaders, England and Germany remain unbeaten.