A goal by Romelu Lukaku on his second Chelsea debut has helped earn the Blues a 2-0 win at London rivals Arsenal, while Harry Kane returned for Spurs but didn't hit the target in their 1-0 win at Wolves.
On a Sunday when Manchester United were surprisingly held 1-1 at Southampton, the return of the big-name strikers Lukaku and Kane helped their London sides maintain their perfect starts to the season.
Lukaku needed only 15 minutes to get off the mark for the Blues after his 97.5 million pounds ($A185 million) transfer from Inter Milan, tapping in a cross from defender Reece James.
The wing-back James then scored Chelsea's second goal himself 20 minutes later, taking his time to fire past goalkeeper Bernd Leno after being found in acres of space by Mason Mount.
Lukaku, who never scored a league goal for the Blues in his first spell, showed why Chelsea were prepared to break their spending record to bring him back to the club seven years after he left London.
The Belgian provided the Blues with the kind of muscular presence in attack they have lacked since the departure of Diego Costa in 2017, both when running at Arsenal's defence and holding the ball up with his back to goal.
Only a reflex save by Leno denied him a second goal when the German palmed Lukaku's point-blank header onto the bar with 15 minutes to play.
Earlier, Kane came off the bench to make his first Tottenham appearance of the season, as uncertainty still swirls around his future with the club.
Dele Alli's ninth-minute penalty was enough to earn Spurs' coach Nuno Espirito Santo victory on his return to Molineux, the home of his former club Wolves.
Kane, who has been heavily linked with a move to Manchester City, entered as a substitute in the 71st minute - to applause from Spurs' travelling contingent - and did nearly add a second goal for them when his close-range shot was saved.
Spurs have won two from two so far this season, both by a 1-0 scoreline.
Manchester United, who had a euphoric start to the season with a 5-1 home win over Leeds, were expected to maintain their 100% start too, but an own goal from Fred on the half-hour mark put them on the back foot at St Mary's.
Jack Stephens dispossessed Bruno Fernandes in the United half and the hosts swiftly moved the ball towards Che Adams, whose shot took a heavy deflection off the Brazilian midfielder to squirm inside the near post and past David de Gea.
United defender Harry Maguire had hit the crossbar early on with a looping header while Anthony Martial's rebound was scrambled off the line by Mohammed Salisu, but Southampton largely dominated, swarming over United with an aggressive high press.
But Ole Gunnar Solskjaer's side levelled early in the 55th when Greenwood thumped a low shot under Southampton keeper Alex McCarthy after clever interplay between Fernandes and Paul Pogba, who added another assist to the five he notched against Leeds.
After the second round of matches, Chelsea and Liverpool are joint-top on goal difference while Brighton and Spurs also have two wins from two.
Australian Associated Press