Pep Guardiola’s impressive side had by far the better of the opening half, but Sterling’s close-range strike was all that they had to show for their supremacy heading into the break.
Though they continued to enjoy considerably more of the ball after the interval, the visitors never quite killed the Magpies off.
And, they were almost made to pay for it late on, as United’s Dwight Gayle steered a downward header just off-target. City held on, though, going 15 points clear at the top of the tree in the process.
Guardiola’s troops wasted no time whatsoever in setting about their business, with United quickly finding themselves camped inside their own half. Sergio Agüero flicked a Fernandinho cross just wide after holding his line, and the Argentine then brought a flying stop out of Rob Elliot after rising high 12 yards out.
Newcastle were struggling to get a kick, but their back five were at least keeping the division’s standout team at bay. As the midway point of the first half passed, the visitors were forced to try their luck from range, Agüero, Danilo and Kevin De Bruyne all taking aim.
Just after the half-hour mark, though, United were undone by a moment of quality. Sterling set off from the left flank and gathered De Bruyne’s delightful ball over the top of the Magpies’ defence, before coolly slotting home via the near post to net for the third game in succession.
Out of nothing, the Magpies proceeded to enjoy a promising spell. After Kyle Walker’s slip, they very nearly drew level, but the backtracking Nicolás Otamendi managed to get a head to Rolando Aarons’ dinked effort, which had looked set to drop in at the back post.
The visitors were soon in the ascendancy once more, though. Just before the break, Elliot got down to his left to keep out another Sterling strike, and early into the second period, the Magpies’ stopper was forced into a similar save, pushing İlkay Gündoğan’s attempt away from goal after the German’s interception 25 yards out.
City continued to knock on the door. De Bruyne nearly struck what would surely have been a decisive second in the 66th minute, getting the better of Elliot but not the near post. Jamaal Lascelles almost headed into his own net during the visitors’ next attack, the defender grateful to see a downward clearance bounce wide of the upright.
Heading into the final ten minutes, though, the Magpies perked up. Substitute Gayle was involved straight away, seeing appeals for a penalty waved away after a coming-together with Danilo. The frontman then took aim from 20 yards, but City’s Eliaquim Mangala managed to block.
For all that the visitors had dominated, United nearly grabbed a point in the last minute of normal time. Christian Atsu dropped a shoulder and delivered an inviting cross, which Gayle – perched six yards out – nodded agonisingly wide of the far post.