Johnson and Palhinha keep Tottenham Hotspur's perfect start going while Bournemouth earn first points of season defeating Wolves.
It took 10 Premier League games for the first cracks to appear in Manchester City's facade last season, but Pep Guardiola got a much earlier reminder of his side's fall from grace on Saturday in another defeat to Tottenham Hotspur.
The optimism of City's opening-weekend romp at Wolverhampton Wanderers quickly evaporated as their first home game of the season ended in a 2-0 loss to the London club.
Goals by Brennan Johnson and new loan signing Joao Palhinha before halftime - the second after a bad error by City keeper James Trafford - gave Tottenham momentum to maintain their great start to the season under new manager Thomas Frank.
Aston Villa are still to register a goal after two games as they went down 1-0 at Brentford while Bournemouth also earned their first points of the season with a 1-0 home win against Wolves.
Burnley ensured that all three promoted clubs have a win after two rounds of fixtures as they beat fellow newcomers Sunderland 2-0 at Turf Moor.
When Tottenham beat Manchester City on the opening day of the 2020-21 season it proved of no consequence as Guardiola's side went on to win the first of four successive titles.
Last season a 4-0 home loss in November was proof that their reign of domination was coming to an end.
Guardiola is beginning a new chapter at The Etihad Stadium with several of his serial trophy winners now having left. But the Tottenham problem remains unsolved.
He has now lost eight of his last 15 matches in all competitions against Tottenham, who always seem to relish facing City whatever the state of their own form.
Tottenham, also at the start of a new journey under Frank, endured a frustrating week as their hopes of signing forward Eberechi Eze from Crystal Palace were ambushed by a rival bid from bitter north London rivals Arsenal.
But they made it six points from six to top the formative table with a disciplined display.
Johnson fired them ahead in the 35th minute from Richarlison's pass and their second was a gift as new keeper Trafford tried to play out from the back but gifted the ball to Richarlison who fed Palhinha to score with a deflected shot.
"Two different teams, two different contexts, but I think both performances were top and both I'll look back on and be very proud," said Frank, whose side beat Burnley 3-0 on the opening weekend.
It was a perplexing day for City who also lost new defensive signing Rayan Ait-Nouri after 22 minutes due to injury.
"I know how we are working and what the players are doing. There are many good things but we have to improve," Guardiola said. "Step by step we will improve and make more connections."
Woe for Wolves
Marcus Tavernier's early deflected strike earned Bournemouth the points at home to Wolves, who suffered a second successive loss. Wolves' cause was undermined by a red card for Toti Gomes early in the second half.
Villa spent a lot of last season challenging for a Champions League spot only to finish sixth and miss out.
There is a sense that they have regressed this season and Saturday's loss at Brentford was a worrying one for Unai Emery.
Brentford's record signing Dango Ouattara scored on his debut, slotting the only goal in the 12th minute after his initial effort was blocked by Emiliano Martinez.
It earned new Brentford manager Keith Andrews, who replaced Tottenham-bound Frank, his first points and continued Brentford's proud record of never having lost their first home game of a top-flight season in 10 campaigns.
Last season it took until October for one of the three promoted clubs to win a Premier League game, with all three eventually going down for the second season in a row.
Burnley's 2-0 win over Sunderland though means they have all had some early reason for optimism.
Josh Cullen opened the scoring after halftime from an assist by Jaidon Anthony and the roles were then reversed as Anthony wrapped it up late on.
On Sunday, Fulham host Manchester United after Everton play Brighton and Hove Albion in their first competitive game at their new stadium at Bramley-Moore Dock stadium. Crystal Palace also host Nottingham Forest.
Champions Liverpool are at Newcastle United on Monday.
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