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.
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.
"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."
"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
