It was an excellent performance from Bournemouth after they took an early lead through the Brazilian via a deflection with just five minutes on the clock, the visitors taking their lead into halftime.
It was a resolute defensive performance from the Cherries, restricting Spurs to just five shots and one on target.
They were a real threat on the break with 19 shots of their own, and possibly should have won by a greater margin, if not for the goalkeeping of Guglielmo Vicario and a handful of missed chances.
But the Cherries held their hosts off to claim their first three points on the road of the season.
Andoni Iraola named an unchanged side from that which beat Wolves last weekend, with eight changes from the Brentford defeat in midweek.
_(Image: John Walton/PA Wire)_ It was a rapid start for the Cherries as they took the lead with the first shot on goal of the match with five minutes on the clock.
Marcos Senesi threaded through a brilliant pass for Evanilson to collect after a diagonal run across the box, and the striker finished via a deflection off Cristian Romero to hand Bournemouth the early lead.
The Brazilian had another shot on goal two minutes later after Antoine Semenyo found him with a squared pass to the top of the D, but he dragged his shot wide.
Bournemouth weren’t far away from a second in the 11th minute as Semenyo headed an outside of the boot cross from David Brooks just over the bar.
Brooks drew a good stop out of Vicario with a free kick that was headed for the bottom corner, before the Welshman headed over from the resulting corner.
Iraola was forced into an early change as James Hill replaced Adam Smith through injury after 25 minutes.
_(Image: John Walton/PA Wire)_ Marcus Tavernier saw his shot blocked after he was slipped in by Semenyo, before Evanilson guided a header just wide after an Adrien Truffert cross from the left.
Spurs tried to pressure the Cherries box before the interval but Bournemouth held them at arm’s length, taking the 1-0 lead into the break and ensuring the hosts had no shots on goal in the first 45 minutes.
The Cherries had a good early chance in the second half as Tavernier headed on a good ball over the top from Senesi, but Semenyo saw his fierce effort saved well behind by Vicario.
Bournemouth went close again as Brooks struck the crossbar after Spurs failed to clear from a throw in, Senesi brought down as he tried to hook the ball into the box.
Brooks then drew another excellent save out of Vicario as he turned and shot in the Spurs box.
_(Image: John Walton/PA Wire)_ Iraola went to his bench shortly after the hour mark, Amine Adli and Ryan Christie replacing Brooks and Alex Scott.
Tavernier shot into the side netting after good work from Christie to burst into the box and cross, before the Englishman had a go from distance but curled the ball over the bar.
Lucas Bergvall shot straight at Djordje Petrovic in Spurs’ first shot on target, before Vicario was again in action to deny Tyler Adams at the near post.
Wilson Odobert blasted a shot over the bar when the ball fell to him in the box with 12 minutes left to play, as Spurs sought an equaliser.
Junior Kroupi and Justin Kluivert replaced goal scorer Evanilson and Tavernier, as the game entered the final ten minutes.
_(Image: John Walton/PA Wire)_ Mathys Tel volleyed wide from the edge of the box as the game entered seven added minutes, before Destiny Udogie headed a free kick wide in the final action of the game as the Cherries won 1-0 to secure their first away points of the season.
**Tottenham Hotspur:** 1, G. Vicario; 24, D. Spence (booked 65’); 37, M. van de Ven (booked, 15’); 17, C. Romero (c); 23, Pedro Porro (Udogie 71’); 30, R. Bentancur; 6, João Palhinha (Bergvall 54’); 29, P. Sarr (Tel 76’); 22, B. Johnson (Odobert 54’); 9, Richarlison; 20, M. Kudus.
**AFC Bournemouth:** 1, Đ. Petrović (booked 72’); 3, A. Truffert; 5, M. Senesi; 18, B. Diakité; 15, A. Smith (c)(Hill 26’ (booked, 90+6)); 12, T. Adams (booked, 88’); 24, A. Semenyo (booked, 12’); 16, M. Tavernier (Kluivert 81’); 8, A. Scott (Christie 64’); 7, D. Brooks (Adli 64’); 9, Evanilson (Kroupi 81’).