Meanwhile, Arsenal have eased fears of being dragged into a relegation battle with a stunning 3-1 win over Chelsea, as Manchester United's Premier League title challenge stumbled after they conceded a late equaliser to draw at Leicester.
Pep Guardiola is optimistic that Manchester City are on course to challenge Liverpool again for the Premier League title after climbing up to fifth and within five points of the leaders with a routine 2-0 win over Newcastle.
At a rain and windswept Etihad Stadium as Storm Bella swept into Manchester, it was plain sailing for the hosts as goals either side of half-time from Ilkay Gundogan and Ferran Torres extended their unbeaten run in all competitions to 10 games.
City's lack of goals has unusually been their undoing so far this season but despite again not hitting the free-flowing heights of previous years under Guardiola, an impressive defensive record is moving them back into contention.
An eighth clean sheet in 10 games never looked threatened against a Newcastle side lacking in intent or threat, with top scorer Callum Wilson left on the bench.
"There are weird results for everyone. This season is about being calm in the good and bad moments," said Guardiola. "I have the feeling we are getting better."
Guardiola's options had been limited prior to kick-off by Kyle Walker and Gabriel Jesus testing positive for coronavirus along with two members of the City staff.
However, the loss of Jesus and Walker is likely to be more keenly felt in the coming week as City travel to second-placed Everton on Monday and Chelsea next weekend in two real tests of their ability to reel in Liverpool at the top of the table.
Aston Villa are another unlikely challenger for the top four as they eased past Crystal Palace 3-0 despite playing the full second half a man down after Tyrone Mings' red card.
Bertrand Traore gave Villa the perfect start but Mings made his teammates work hard for the win when he was sent off for two clashes with Wilfried Zaha.
Ignoring that setback, Kortney Hause and Anwar El Ghazi wrapped up the points for Villa.
Fulham edged to within a point of safety with a 0-0 draw at home with Southampton.
"We played at the tempo we have to play. We are a team that needs to make a lot of passes, not run so much and attack in the right moments. Today our positional game was perfect," added Guardiola.
"Unfortunately we could not score more goals but it is a good result and three more points. We don't have much time to think about it because in 45, 46 hours we are back."
City threw away two points in their last home game in a 1-1 draw with West Brom after Gundogan opened the scoring.
But there was no repeat this time after the German midfielder was picked out by Raheem Sterling for a tap-in.
Even Kevin De Bruyne has suffered from a lack of confidence in front of goal in recent months as City's routine thrashings of sides in the lower reaches of the table have dried up.
The Belgian is yet to score from open play this season and paid for his hesitation as he look ed for a teammate to square the ball to when clean through on Karl Darlow as the Newcastle 'keeper kept his side in the game before half-time.
City's pressure finally told for the all-important second goal 10 minutes into the second half as Joao Cancelo's low cross was turned into the path of Torres by Federico Fernandez and the Spaniard applied the simple finish.
That made it just the third time in 12 league games that City had scored more than once and there should have been far more in the final half-hour as conditions worsened.
Sterling, Bernardo Silva and substitute Sergio Aguero all missed glorious opportunities from close range to give the scoreline a fairer reflection.
Arsenal win 3-1 against Chelsea
Arsenal have eased fears of being dragged into a relegation battle with a stunning 3-1 win over Chelsea as Manchester United's Premier League title challenge stumbled after they conceded a late equaliser to draw at Leicester.
Everton moved into second place, two points behind leaders Liverpool with a 1-0 win at Sheffield United, while Manchester City climbed to fifth place after beating Newcastle 2-0.
Liverpool will go five points clear of Everton if they beat struggling West Brom on Sunday.
Mikel Arteta led Arsenal to win the FA Cup the last time they faced Chelsea in August, but less than five months on the Spaniard was under intense pressure after a run of one win in 10 league games.
Arteta had bemoaned his side's fortune in recent weeks, but the Gunners' luck turned on a night when he gave youngsters Gabriel Martinelli and Emile Smith Rowe the chance to shine in the absence of more experienced figures such as David Luiz, Willian and Pierre-Emerick Aubameyang.
"It's a really big win for us," said Arteta. "Hopefully it is going to be a turning point and elevate the level of confidence in the team."
Kieran Tierney won a soft penalty for a push by Reece James and Alexandre Lacazette slotted home the spot-kick to open the scoring on 34 minutes.
Granit Xhaka then answered his critics after being stupidly sent off in a 1-0 defeat by Burnley earlier this month with a brilliant free-kick to double Arsenal's lead just before half-time.
A third consecutive away loss for Chelsea further damages their chances of competing for the title and there was no way back for Frank Lampard's men once Bukayo Saka chipped in off the inside of the post 11 minutes after the break.
"It's not good enough," said Lampard. "The players have got to take responsibility."
Tammy Abraham did pull a goal back five minutes from time and Chelsea could have set up a grandstand finish in stoppage time, but Jorginho's penalty was saved by Bernd Leno.
Victory lifts Arsenal up to 14th, six points clear of the relegation zone, while Chelsea drop down to sixth on goal difference.
Manchester United miss out
Manchester United missed out on equalling a Premier League record of 11 straight away wins as for once this season they paid for not finishing strongly in a dramatic 2-2 draw.
Ole Gunnar Solskjaer's men had come from behind in each of their previous away league games this season, but twice went in front at the King Power Stadium through Marcus Rashford midway through the first half and Bruno Fernandes 11 minutes from time.
"One point is not the worst result but we are disappointed we didn't get away with three," said Solskjaer.
Harvey Barnes' blistering strike levelled for Leicester before half-time and United were undone by Jamie Vardy's movement in the box as the veteran striker latched onto Ayoze Perez's cross and saw his shot deflect in off the u nfortunate Axel Tuanzebe.
At Bramall Lane, Gylfi Sigurdsson killed off the bottom of the table Blades on 80 minutes with a clinical finish.
That sealed Everton's fourth successive league win and set up a significant clash with Manchester City on Monday.
"This team has a lot of spirit. I'm really pleased to manage these players," Everton boss Carlo Ancelotti said.