The relief was clear in the wild celebrations deemed excessive by the referee. Having already been booked, Sterling saw red after receiving a second yellow card.
There could be further recriminations. After police announced an investigation into the melee during the celebrations, City striker Sergio Aguero responded to video circulating on Twitter by posting: "About their steward, I did not hit anyone, this allegation is false, and the tv pictures prove it."
While City has collected seven points out of a possible nine, Bournemouth slumped to a third consecutive loss.Crystal Palace and West Ham are also winless. Palace was beaten by Swansea 2-0, while West Ham lost at Newcastle 3-0.
Newcastle picked up its first points along with fellow newcomer Brighton, which drew with 10-man Watford 0-0. Huddersfield extended the unbeaten start to its first Premier League campaign by holding Southampton 0-0.
CITY FIGHTBACK
City recovered after falling behind when Charlie Daniels spectacularly struck into the roof of the net from a tight angle. Gabriel Jesus leveled in the 21st minute but it took until Sterling's late deflected strike for City to prevail, triggering the outpouring of exuberance.
Sterling had already been booked and was shown a second yellow card.
"If you cannot celebrate with the fans the best solution is not to invite the fans," City manager Pep Guardiola said. "You can imagine how happy he is, how happy the fans are."Some spilled onto the pitch, with two arrested. Police officers also held back Benjamin Mendy and exchanged words with Aguero."Officers are reviewing CCTV of the pitch encroachment as part of an ongoing investigation to establish whether any other offences may have been committed," Dorset Police said in a statement. "This investigation is in the very early stages."
SUBSTITUTES DELIVER
At Old Trafford, Leicester was proving hard for United to break down. Even when the hosts won a penalty, Romelu Lukaku's spot kick was saved.Then the substitutes started to arrive and quickly delivered. After less than three minutes on the pitch, Rashford netted in the 70th from Henrikh Mkhitaryan's corner.Mkhitaryan then made way for Fellaini, who was on target in the 82nd with a goal all the substitutes played a part in. Rashford sent the ball down the left flank to Jesse Lingard, who had replaced Anthony Martial, and his shot was turned in by Fellaini from close range.
BENITEZ BOOST
Newcastle lost its opening matches to Tottenham and Huddersfield without scoring but managed to hit three against West Ham for its first win. Joselu, Ciaran Clark and Aleksandar Mitrovic scored to lift the gloom surrounding Rafa Benitez's side.
DE BOER DESPAIR
Palace isn't only winless at the start of Frank de Boer's reign as manager. The south London club also hasn't scored. Tammy Abraham and Jordan Ayew did net for Swansea at Selhurst Park as the south Wales club claimed its first win.
UNBEATEN WATFORD
Watford was a man short from the 24th minute against Brighton, after Miguel Britos was sent off for a studs-up tackle on Anthony Knockaert, but still prolonged its unbeaten start. It was a third red card in 20 league games for Britos.Brighton hit the woodwork twice, but a draw did enable the south-coast club to collect its first point in the topflight since 1983.
