Manchester City climbed to third in the Premier League table, closing the gap on Liverpool to just two points after a Phil Foden-inspired victory over Sheffield United, extending their imperious head-to-head record to 12 games without defeat (nine wins, three draws).Heading into this match, City had conceded first in four of their last five Premier League encounters (two wins, two draws, one loss) – a concerning habit Pep Guardiola was no doubt keen to see the back of. In typical fashion, the hosts dominated possession, and after some patient probing, they made the breakthrough when Foden laid off Rodri, who drove at the Blades’ backline and picked his spot with a low strike.Foden was involved again shortly after when he slipped in Bernardo Silva, whose shot from a tight angle was turned behind before Kyle Walker curled an effort from distance wide of the mark against his boyhood club. A pair of late first-half chances was the best the visitors could muster, with William Osula forcing Ederson into his first stop.Baby, it’s Cole outsideHaving failed to find the net in the first half, Chris Wilder’s side remain the only Premier League team yet to score in both halves of a league match this season. Nonetheless, a one-goal deficit meant that they remained in the contest as City continued where they left off after the break. In the thick of the action, Foden was posing plenty of problems for the Blades, and after a neat pass from Oscar Bobb set him free in the box, the England international picked out a sliding Julián Álvarez at the back post, marking his 50th Premier League appearance with a goal.City maintained control of the match to see out a comfortable victory against Sheffield United, who are yet to keep a Premier League clean sheet on their travels this campaign as they continue to prop up the table, seven points adrift of 17th-placed Everton. Meanwhile, a win here means that City haven’t lost a home head-to-head encounters since 1987 (nine wins, five draws), last conceding a goal in 1991, as they move above Arsenal in an increasingly intriguing title race.Elsewhere, Aston Villa climbed to second in the Premier League table, level on points with leaders Liverpool thanks to a 3-2 victory over relegation-battling Burnley, as Unai Emery became the first Villa manager since Martin O’Neill in 2010 to mastermind a home win against the Clarets.To say the opening stages of this game were entertaining would be a far cry from the truth, but with the incentive of taking a joint lead of the Premier League, Villa eventually wrestled a stranglehold on proceedings. There were few prizes on offer for guessing who was at the heart of it – Ollie Watkins – but he could only direct a fierce volley into the grateful hands of James Trafford. Villa pressure was incessant at times, but while they still hadn’t taken the lead, the door was gently ajar for Burnley, who almost burst through it when Josh Brownhill twice came close.##EDITORS_CHOICE##The Clarets were left to rue those missed opportunities just moments later too, when Watkins squared for Leon Bailey to fire the hosts ahead. That only proved to be a temporary advantage for Villa though, who were soon pegged back after Zeki Amdouni thundered home Dara O’Shea’s knockdown from close range to silence Villa Park. But as has so often proved to be the case for Burnley this season, they threw away their reprieve in typically calamitous circumstances. One long pass from back to front took out the whole Clarets defence and Watkins laid the ball on a plate for Moussa Diaby to fire Villa into a halftime lead.It would be fair to say the opening exchanges in the second half went the way of Burnley, who were starting to build up a head of steam – one that was quickly extinguished when Sander Berge was shown a second yellow card. It was copy-and-paste stuff as far as Villa were concerned, raining ball after ball into the Burnley box, but for all their pressure, it was the Clarets who incredibly forced their way back into the game. That goal held so much meaning too, as Lyle Foster broke in behind and slammed home at the near post – his first goal since returning from a mental health lay-off.Frustration around Villa Park was audible after that equaliser, with Emery himself also looking visibly shaken in response to the moans and groans from the Villa faithful. That didn’t deter the players, who pushed and probed for a winner which ultimately arrived in the dying moments when Douglas Luiz stroked home from the penalty spot, breaking Burnley hearts and securing Villa a share of the Premier League lead.PREMIER LEAGUE – MATCHDAY 20SaturdayLuton Town – Chelsea 2-3 (0-2)/Barkley 80, Adebayo 87 – Palmer 12, 70, Madueke 37/Aston Villa – Burnley 3-2 (1-1)/Bailey 29, Diaby 42, Douglas Luiz 90 – Amdouni 31, Foster 72/Crystal Palace – Brentford 3-1 (1-1)/Olise 14, 58, Eze 39 – Lewis-Potter 2/Man.City – Sheffield Utd 2-0 (1-0)/Rodri 14, Alvarez 61/Wolverhampton – Everton 3-0 (1-0)/Kilman 25, Cunha 53, Dawson 61/20:30: (3.35) Nott.Forest (3.45) Man.Utd. (2.15)Sunday17:00: (1.80) Tottenham (3.80) Bournemouth (4.30)17:00: (6.25) Fulham (4.10) Arsenal (1.60)Monday23:00: (1.50) Liverpool (4.50) Newcastle (7.25)Tuesday22:30: (2.50) West Ham (3.45) Brighton (2.75)***odds are subject to change***