James Maddison scored his first Tottenham goal and delivered an outstanding individual performance as Spurs continued their fine start to life under Ange Postecoglou with victory at Bournemouth.
Maddison's opener came at the end of a flowing Spurs move involving Yves Bissouma and Pape Sarr, and arrived just moments after Cherries goalkeeper Neto had kept out another effort from the 26-year-old.
Spurs carved out the better opportunities before half-time but Richarlison - who endured a frustrating afternoon - was unable to open his tally for the season despite finding himself in some excellent goalscoring positions.
Bournemouth made a bright start to the second half and Antoine Semenyo nearly followed up his goal at Anfield last weekend with a superb second-half equaliser, but the Ghanaian's curling effort from the edge of the box flew narrowly wide of the top corner.
Young full-back Destiny Udogie was the architect of the visitors' second, playing an excellent one-two with Heung-min Son before cutting the ball back for Dejan Kulusevski, who found the far corner for his first of the campaign.
Spurs have seven points from their opening three league games, while Bournemouth's wait for a first win of the season goes on after slipping to a second straight defeat.
Maddison sensational for Spurs
To say Maddison has hit the ground running at Tottenham would be doing the former Leicester man a great disservice.
The England international followed up his two assists in the opening-day draw at Brentford with another influential display in victory over Manchester United, and he was superb once again on the south coast as Spurs continued their unbeaten start.
Often dropping deep to collect possession, Maddison was at the heart of the visitors' best attacking moves and could have scored seconds before his right-footed opener, but Neto - whose hasty clearance had gifted Spurs possession - atoned for his error.
Richarlison spurned two good chances to double Tottenham's lead - both from superb Maddison balls - the Brazilian dallying long enough to give Bournemouth time to clear before sending a close-range header into the side-netting.
That first opening in particular summed up a disappointing afternoon for the former Everton player, who lost the ball cheaply on several occasions before being replaced by Pierre-Emile Hojbjerg on the hour mark.
Udogie, a £15m summer signing from Udinese, took a leaf out of Maddison's book for Tottenham's second, linking up wonderfully with Son before darting to the byline and pulling the ball back for Kulusevski.
Maddison missed a late chance to add a third for Spurs but it mattered little on a comfortable afternoon for Postecoglou's team, whose fans were singing "we've got our Tottenham back" moments before the full-time whistle.
Cherries second best
Midfielder Tyler Adams - a recent signing from relegated Leeds - was introduced to the Vitality Stadium crowd before kick-off on Saturday afternoon.
The USA international remains sidelined with a longstanding hamstring issue, but Andoni Iraola's side could have done with his presence in the first half as Maddison ran the show.
Despite struggling to contain the 26-year-old before the interval, the Cherries very nearly ended the half on level terms after Philip Billing sent a curling, left-footed strike narrowly wide of the far post.
Ryan Christie also tested Tottenham goalkeeper Guglielmo Vicario's reflexes with a stinging drive from the corner of the area, before Semenyo's excellent effort just missed the angle between bar and post.
Iraola will be frustrated at the manner of the visitors' second, with several of his defenders guilty of ball-watching as Udogie worked his way to the byline and crossed for Kulusevski.
Bournemouth have shown glimpses of promise under Iraola but victory continues to elude the Cherries, whose start to the campaign is not about to get any easier.