City dominated with 80 percent possession, but had to wait until the 84th minute when Sterling unwittingly bundled home after a shot from Gabriel Jesus cannoned off goalkeeper Jonas Lossl and into his path.
In front of their vociferous fans, Huddersfield -- who earlier this month beat City's rivals United -- took the most unlikely lead when Nicolas Otamendi diverted a corner into his own net in first half stoppage time.
Their lead was erased within two minutes of the restart, however, when Sergio Aguero calmly converted a penalty after Sterling was brought down by Scott Malone.
Huddersfield's Rajiv van La Parra was shown a red card after the final whistle following an altercation with Leroy Sane.
Sterling's 12th goal of the season ensured Pep Guardiola's all-conquering side moved on to 37 points from 13 games, eight ahead of nearest challengers Manchester United and 11 clear of champions Chelsea in third place.
It also extended their extraordinary sequence of wins in all competitions to 18 while they also remain unbeaten in their last 26.
"We came in at halftime disappointed, we wanted to get something out of the game and that's what we have done," Sterling told Sky Sports.
In sweeping all before them in the Premier League this season, City had scored 40 goals in their first 12 sensational displays of attacking football.
They were expected to do much the same against newly-promoted Huddersfield but the anticipated rout never materialised.
Having defended heroically throughout a first half in which City were dominant, Huddersfield took the lead when Otamendi was unable to react fast enough to prevent Christopher Schindler's header clipping his shoulder and deflecting in.
Yet City restored parity within seconds of the restart through Aguero's ninth league goal of the season.
Huddersfield, who sit 11th in the table with 15 points, appeared on course for a very credible point until a lucky intervention saw Sterling bundle home late-on to cap his man-of-the-match display.
(Reporting By Tom Hayward; Editing by Ian Chadband)
