Just 12 months ago, Arsenal lost their first three league games in the club's worst start to a season for 67 years.
This year the Gunners sit in pole position after opening the campaign with a third successive victory.
"Compared to last season we are a little bit ahead," said Arsenal midfielder Martin Odegaard, who scored twice in the first 11 minutes.
"But we have to stay calm, stay humble, keep working hard and see where it takes us."
It is too soon to declare Arsenal the finished article, but the derision that accompanied Mikel Arteta's men when they squandered a golden opportunity to qualify for last season's Champions League has been erased by their strong start this term.
After scoring four against Leicester last weekend, this was another swashbuckling display from the north Londoners.
Arsenal went ahead after five minutes as Gabriel Jesus' superb run and pass found Gabriel Martinelli whose shot was pushed into the path of Odegaard for a simple finish.
Odegaard netted again six minutes later when Jesus' heavy touch fell kindly for the Arsenal captain to fire home from 10 yards.
William Saliba's 54th minute goal, a superb first-time curler from the edge of the area, epitomised the confidence pulsing through Arsenal as the French defender claimed his first goal for the club.
Second-placed Tottenham have also made a strong start after backing Antonio Conte heavily in the transfer market in his first full season in charge.
After snatching a place in the Champions League from Arsenal in May, Tottenham have kept the momentum going with seven points from their first three games.
However, Conte was still displeased with a sloppy first-half performance that could have been punished by more potent opponents.
Tottenham improved markedly after the break and got their reward when Kane bulleted home a header after Ivan Perisic flicked on Son Heung-min's corner.
Kane's 185th Premier League goal -- his 250th in all competitions for Tottenham -- set a record for the most scored by anyone for a single club, edging ahead of Sergio Aguero's 184 for Manchester City.
"I think every single player is ready to exchange a personal achievement to reach a trophy," said Conte on Kane, who is yet to win a major trophy in his career.
"We're working on this aspect. The path is difficult, the path is long, but we have to try to do this."
Fofana left out for Leicester
At the other end of the table, Manchester United remain bottom ahead of their huge clash against Liverpool on Monday.
But Leicester are only one point better off after Southampton's Che Adams came off the bench to score twice in a 2-1 win at the King Power Stadium.
Wesley Fofana was left out of Brendan Rodgers's squad as the Frenchman seeks to force through a move to Chelsea.
Leicester are the only Premier League club yet to spend any money in the transfer window, but may have to in the final 10 days of the window to ward off a difficult season.
James Maddison's free-kick had put the Foxes in front, but Adams twice pounced on poor defending in the absence of Fofana to give Southampton their first win of the season.
The pressure is also back on Aston Villa manager Steven Gerrard after his side threw away a perfect start to lose 3-1 at Crystal Palace.
Ollie Watkins opened the scoring for the visitors at Selhurst Park after five minutes, but Wilfried Zaha quickly levelled.
Zaha then put Palace in front at the second attempt after his penalty was saved by Emiliano Martinez.
Jean-Philippe Mateta made the points safe 19 minutes from time.
Fulham remain unbeaten on their return to the top flight as Aleksandar Mitrovic's powerful header won a thrilling west London derby against Brentford 3-2.
Everton secured their first point of the season thanks to Demarai Gray's late equaliser to cancel out Brennan Johnson's goal for free-spending Nottingham Forest in a 1-1 draw at Goodison Park.
