Walters had a nightmare afternoon at the Britannia Stadium, putting through his own net with a diving header on the stroke of half-time and beating Stoke keeper Asmir Begovic again with a header from a corner just past the hour. He also missed a late penalty.
Stoke have not beaten Chelsea in the league since 1975, and Frank Lampard's penalty and a fine Eden Hazard goal put the Londoners one point ahead of fourth-placed Tottenham Hotspur, who drew 0-0 at Queens Park Rangers in the lunchtime kick-off.
Rangers prop up the standings after Reading staged a remarkable comeback to beat West Bromwich Albion 3-2, scoring three times in the last eight minutes after trailing to Romelu Lukaku's double.
Aston Villa dropped into the bottom three following Southampton striker Rickie Lambert's contentious first-half penalty that secured their fellow strugglers a 1-0 victory at Villa Park.
Chelsea moved within four points of City, and 11 behind United, after getting a helping hand - or head - at Stoke, normally ferocious opponents on home turf.
Amid growing discontent among Chelsea fans still seething at the Spaniard's appointment and his team's inconsistent performances, Benitez said the atmosphere in the squad was good.
In their previous two games Chelsea suffered a shock home league defeat by QPR followed by a midweek loss to Swansea City in the first leg of the League Cup semi-final at Stamford Bridge.
"We are working very hard, the players are happpy - you can see they are enjoying playing football," Benitez told Sky Sports.
"Obviously you cannot control all the results but the atmosphere is fantastic - hopefully we can win one or two more games and people will realise that we are progressing and doing well."
Chelsea also got a boost on Saturday with the return to first-team action of captain John Terry after two months out with a knee injury.
Terry replaced Juan Mata after 79 minutes, although he did concede the late penalty that Walters struck against the top of the bar.
Reading gave their fans hope that they can stay up with an unlikely win over West Brom at the Madejski Stadium.
Until the 82nd minute they had been run ragged by on-loan striker Lukaku, but Jimmy Kebe started a memorable comeback. Adam Le Fondre then equalised from the penalty spot with two minutes to go before Pavel Pogrebnyak pounced in the last minute.
"We were really resilient. We have got great character," Reading manager Brian McDermott said.
The main talking point at Villa Park surrounded Lambert's 34th-minute penalty, which earned Southampton the three points. Enda Stevens was penalised for bringing down Jay Rodriguez and both managers agreed the decision was harsh.
"Enda Stevens was not even close to him and that is the most hurtful th
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