Marcus Rashford was back among the goals as Manchester United moved to within a point of Manchester City with a 1-0 win at the Etihad.
United took the lead in the 16th minute through a brilliant piece of skill from Rashford. After being played in by Juan Mata, the 18-year-old left Martin Demichelis on the deck with a neat turn before coolly slotting past Hart.
City then lost Sterling just before the half-hour mark after he picked up a knock in a challenge with Mata.
United thought they should have had a penalty in first-half stoppage time when Demichelis appeared to step into Rashford’s path, but referee Michael Oliver waved away the claims.
Hart was forced off shortly after half-time after he was involved in a collision with Anthony Martial, who was chasing down Demichelis’ poor backpass.
City started to increase the pressure looking for an equaliser as Sergio Aguero headed against the post before Wilfried Bony missed his kick in front of goal.
But there was no way back into the game as United moved level on points with fifth-placed West Ham, and to within just one point of City in the final Champions League berth.
Tottenham Hotspur reduced Leicester City’s lead at the top of the table back to five points with a convincing 3-0 win at home to AFC Bournemouth.
Spurs were in front after just 44 seconds through Harry Kane, sliding in to guide home a superb cross from Kyle Walker.
And the second goal came after 16 minutes, another for Kane with a left-footed finish from inside the box after he had been played in by Dele Alli. That goal took him clear at the top of the Premier League goalscoring chart with 21.
It was three seven minutes after the break. Kane’s long-range shot was parried by Artur Boruc, and Christian Eriksen was on hand to tap in the rebound from close range.
The home win for Spurs was never in doubt as they continue to chase Leicester in a bid for a first Premier League title.
In other results, Southampton came from two goals down to defeat Liverpool 3-2, and Newcastle and Sunderland battled to a 1-1 draw.