Second-half goals from Bernardo Silva and substitute Leroy Sane gave Manchester City a 2-0 derby triumph over Manchester United as Pep Guardiola’s men edged back ahead of Liverpool in the Premier League title race.

Following a humiliating 4-0 defeat at Everton on Sunday, Ole Gunnar Solskjaer made five changes to the United XI, and he was rewarded with an enterprising first-half display.

But PFA Player of the Year nominee Silva broke the deadlock in the 54th minute and Sane gave the off-colour David de Gea another moment to forget 12 minutes later.

City are a point ahead of Liverpool, knowing victories in their final three games will guarantee back-to-back titles, with two-thirds completed of an unprecedented domestic treble.

Jesse Lingard volleyed wide from Paul Pogba’s exquisite 16th-minute pass as an end-to-end contest began to develop – De Gea beating away Silva’s rasping drive before United sprang up the field and Marcus Rashford was denied by an alert Ederson.

City gradually found their poise as half-time approached, with De Gea thwarting Raheem Sterling at the end of a deft move in the United box.

Fernandinho hobbled off injured after making a brilliant tackle on Pogba early in the second half.

Sane’s introduction meant Ilkay Gundogan dropping back to the base of the midfield and Silva dropping into a central role, and the two men combined in their new positions as the Portugal international caught out De Gea at his near post.

Sergio Aguero then hit a rasping shot against the outside of the same upright, but Lingard passed up a chance to level when Rashford’s bouncing ball across goal evaded Vincent Kompany and the England midfielder.

Sterling’s charge around Fred to tee up Sane was the nerve-settling moment City required and United’s earlier verve evaporated as a result.

What does it mean? Advantage City in relentless title charge

Chelsea can report on the potential woes of facing a motivated Burnley, while Leicester City boss Brendan Rodgers might fancy flipping the 2013-14 narrative when his side visit the Etihad Stadium on May 6.

City then close against a Brighton and Hove Albion side who could still be scrapping for their Premier League lives. But, however much United might have diminished from the side who retained the title in 2008-09 – no team has done it since – it is hard to escape the feeling Guardiola has negotiated his biggest remaining challenge.

Arsenal’s defeat at Wolves means United’s stumbling top-four bid still has life, despite having lost seven of their last nine games across all competitions.

Ederson poise pivotal to City triumph

At times this season, Ederson has looked like City’s most involved spectator – looking on as goals are rattled at the other end. But twice in the space of a week he has stood up to show razor-sharp instincts and flawless handling to set up pivotal wins. The Brazilian did not have to make the eye-catching saves he made versus Tottenham at the weekend, but he was a calming influence for a jittery City before the interval, making the match a tale of two goalkeepers.

Near-post woes deepen De Gea’s malaise

United’s outstanding performer of the post-Alex Ferguson years, the Spain goalkeeper is undergoing a dire period. After dropping a speculative Lionel Messi shot into his net at Camp Nou last week and shipping four at Goodison Park, there were suspicions he might have done better with Silva’s opener. That his attempts on Sane’s goal amounted to a howling error was beyond doubt.

What’s next?

City travel to Burnley on Sunday, while United are back at Old Trafford for another crunch clash against Chelsea.