Arsenal, despite a raft of injuries, moved ahead of Leicester, who drew 1-1 at Aston Villa on Saturday. Both teams have 44 points from 22 matches but the London side’s goal difference is three better than the Foxes.
Manchester City are a point behind the leading pair after they beat Crystal Palace 4-0 on Saturday, while Tottenham Hotspur complete the top four with 39 points following their 4-1 home win over Sunderland also on Saturday.
Manchester United are next on 37 points, moving up one place after Rooney’s 78th minute volley gave them victory at arch-rivals Liverpool in a drab north-west derby which improved slightly after the break following a poor first half.
Rooney struck after a header by Marouane Fellaini rebounded straight to him off the bar with the United skipper giving keeper Simon Mignolet no chance with his ferocious strike.
Arsenal, ravaged by injuries and without in-form playmaker Mesut Ozil, their latest casualty with a slight foot problem, on Sunday, have not won at Stoke for six years but came close to ending that run with three excellent attempts.
However, they could not find a way past young England international keeper Jack Butland who made important saves from Alex Oxlade-Chamberlain and Olivier Giroud, twice.
Arsenal manager Arsene Wenger, who has seen his side beaten three times at Stoke in the last five seasons, said he was pleased with a point after dropping two to a last-minute equaliser in a 3-3 draw at Liverpool on Wednesday.
“We have had two very physical games in four days away from home. Stoke wanted to surprise us and made it very physical from the start and we had to fight,” he told Sky Sports.
Arsenal keeper Petr Cech, the Man of the Match, was far busier in the second half, denying Marko Arnautovic twice, Bojan Krkic and Joselu as Stoke poured forward looking for a third successive home league win over the Gunners.
Stoke remain seventh with 33 points.
Most of the build-up on Sunday was focussed on the Liverpool versus United clash, hailed by the media as the biggest rivalry in English football between two clubs who have won 38 domestic league titles between them.
In reality, though, it lacked all the intensity of games in the past when both were challenging for the title or top four places with the defeat leaving Liverpool trailing in ninth place, eight points behind the Champions League spots.
“I didn’t see too many chances for Manchester United and we didn’t take ours. Of course it is frustrating,” Liverpool manager Juergen Klopp told the BBC.
United manager Louis van Gaal added: “We have made a good start in 2016, to beat Liverpool for the second time in a row is marvellous, it gives a big boost for the players and the fans so I hope we shall continue with winning.
“That is why we are here, to win our games and at the end of the season to be in the first three positions in the league.”
Rooney’s winner was his 176th league goal for United, a record for a player for one club in the Premier League era, following his 15 league goals for Everton at the start of his career.
His United total has eclipsed the previous record of 175 set by Thierry Henry for Arsenal in his two spells in north London between 1999 and 2012.