City, without several first-team regulars including captain Vincent Kompany and striker Sergio Aguero, took the lead in the 16th minute when Sterling fed David Silva with a clever backheel in the box and the Spain playmaker drove home a bullet shot.
Gladbach, in confident mood after inflicting Bayern Munich's first Bundesliga defeat of the season at the weekend, then took command with their slick-passing style and were 2-1 up by halftime.
Julian Korb equalised with a right-foot shot in the 19th minute, after a surging run from Fabian Johnson, before Brazilian Raffael scrambled the ball home from close range in the 42nd following another neat passing move.
City, who had never finished top of a Champions League group before, perked up after the break and it was no surprise when Sterling converted from close range after overlapping right back Gael Clichy pulled the ball back from the byline in the 80th minute.
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A minute later substitute Wilfried Bony set Sterling up and the former Liverpool forward provided a delightful curling effort from 16 metres.
Bony made it 4-2 from a left-wing cross by Aleksandar Kolarov in the 85th minute as City, who had already clinched their place in the knockout stages, ended the group stage with 12 points from six games.
Juventus, beaten 1-0 at Sevilla on Tuesday, also qualified for the Champions League last 16 on 11 points.
Europa League holders Sevilla ended up with six points and again go into Europe's second-tier club competition after finishing in third place. Gladbach were bottom of the group with five points.
(Writing by Tony Jimenez; Editing by Toby Davis)
