Winning his 59th cap, Sterling bagged his 14th goal for the national team, cutting in from the left to hit a slightly deflected shot past the keeper on 31 minutes.
James Ward-Prowse had put the Three Lions ahead with Dominic Calvert-Lewin adding a second.
Sterling could have scored more goals after going close with a couple of long range efforts but was rested at the break with further games against Albania and Poland to come in the coming days.
John Stones almost bagged his third international goal in the first half but half-volleyed over from close range.
Stones was also rested at the break, with Phil Foden one of four subs who came on for the second half with England 3-0 up at that point.
Foden was his usual lively self, playing down the right wing and later on the left as he showed Gareth Southgate his versatility in attack.
Calvert-Lewin got a second before Foden assisted Ollie Watkins who marked his England debut with a goal to make it 5-0 on 83 minutes to start the World Cup qualifying campaign off in style.
Goal-machine Ilkay Gundogan was on target for Germany who beat Iceland 3-0.
It was Gundogan‘s 18th goal for club and country in what has been a phenomenal campaign for the City midfielder.
He struck on 56 minutes with a shot into the bottom left corner of the net from 20 yards out.
Elsewhere, three City players were in action for Spain against Greece.
Rodrigo, Eric Garcia and Ferran Torrres all started for La Roja who will be disappointed by the 1-1 draw with the Greeks.
Torres lasted 72 minutes before being subbed, while Garcia and Rodrigo completed 90 minutes.
Zack Steffen was also in action as USA beat Jamaica 4-1 in a friendly played in Austria,
