In a first half that lacked attacking quality, a moment of brilliance from Bournemouth and Kroupi handed them the advantage at the break with an excellent half-volley.
Wolves saw much of the ball in the second half as they sought an equaliser, but the Cherries absorbed the pressure and doubled their lead as the game entered stoppage time through Scott.
Bournemouth's Eli Junior Kroupi celebrates scoring their side's first goal of the game during the Premier League match at Molineux Stadium, Wolverhampton. (Image: Jacob King/PA Wire)
Andoni Iraola named an unchanged side from the team which beat Liverpool last weekend, as new arrivals Rayan and Christos Mandas were among the substitutes.
Wolves saw a goal disallowed after six minutes after Mateus Mane finished after a mishit shot from Rodrigo Gomes, but the latter was offside when he made his run in behind.
Kroupi saw a shot from outside the box on the left go wide in Bournemouth’s first attempt on goal, before Mane shot straight at Djordje Petrovic from range.
Amine Adli shot high and wide after some neat build up from the Cherries, before Mane fired at the Bournemouth keeper once again after a quick break from the hosts.
Bournemouth's Amine Adli shoots at goal during the Premier League match at Molineux Stadium, Wolverhampton. (Image: Jacob King/PA Wire)
In a half lacking some attacking quality from either side, the visitors to Molineux took the lead with a brilliant piece of attacking play.
Scott cut out a pass out from the back, beat one man before he played it to Adli and he flicked it on to Kroupi who took a touch before powering the ball past Jose Sa on the half-volley.
Sa denied Adli with an excellent save after the Moroccan went around the keeper but had a tight angle with which to finish, and the Portuguese was able to scramble back and save behind.
Bournemouth's Eli Junior Kroupi celebrates scoring their side's first goal of the game during the Premier League match at Molineux Stadium, Wolverhampton. (Image: Jacob King/PA Wire)
The Cherries held their one-goal lead into the interval and they had a good chance in the first minute of the second period.
Alex Jimenez charged forward down the right wing and burst into the box before he shot, but Sa saved behind.
After that chance, Wolves saw much more of the ball as they attempted to apply pressure and find an equaliser.
Tolu Arokodare shot straight at Petrovic after winning the ball off James Hill, before Hee Chan Hwang had a go from a free kick but it was comfortable for the Serbian.
Bournemouth's James Hill (left) and Wolverhampton Wanderers' Tolu Arokodare battle for the ball during the Premier League match at Molineux Stadium, Wolverhampton. (Image: David Davies/PA Wire)
Petrovic saved brilliantly with his legs from Arokodare as he turned a cross from the left towards goal after the Wolves forward had sliced an effort well wide.
Rayan was introduced alongside Ryan Christie for his Cherries debut, as that pair replaced Kroupi and Adli with 22 minutes to play.
Wolves substitute Jorgen Strand Larsen shot wide after Petrovic saved a Joao Gomes shot following a corner in a big chance for the hosts.
Arokodare missed another gilt-edged chance when he took too long over a shot when found in space and shot wide.
Bournemouth's Alex Scott (left) and Wolverhampton Wanderers' Joao Gomes battle for the ball during the Premier League match at Molineux Stadium, Wolverhampton. (Image: David Davies/PA Wire)
Joao Gomes hit the post from a corner as the hosts applied the pressure in search of an equaliser.
Alex Toth and Enes Unal replaced Jimenez and Evanilson, and the Hungarian’s first action was to fire into the side netting after a rapid counterattack.
As the game entered five added minutes, the Cherries doubled their lead.
Rayan picked up an assist on debut as he was found on the left of the box by Adrien Truffert, he got to the byline before cutting the ball back for Scott to smash the ball into the roof of the net.
Bournemouth's Alex Scott scores their side's second goal of the game during the Premier League match at Molineux Stadium, Wolverhampton. (Image: Jacob King/PA Wire)
Arokodare again headed straight at Petrovic as the Cherries held firm for a clean sheet and their first away win since their 1-0 win at Spurs at the end of August.
That takes Bournemouth to four games unbeaten and onto 33 points.
Wolves: 1, J. Sa; 15, Y. Mosquera (booked, 61’); 4, S. Bueno (Lima 89’); 12, E. Agbadou; 3, H. Bueno (Moller Wolfe 89’); 7, Andre (booked, 45’)(Arias 80’); 8, J. Gomes (booked, 75’); 36, M. Mane; 21, R. Gomes (Bellegarde 71’); 11, H. Hwang (Strand Larsen 71’); 14, T. Arokodare.
AFC Bournemouth: 1, D. Petrovic; 15, A. Smith (c)(Diakite 90+4’); 23, J. Hill (booked, 88’); 5, M. Senesi; 3, A. Truffert; 8, A. Scott; 4, L. Cook; 20, A. Jimenez (booked, 58’)(Toth 85’); 22, J. Kroupi (Christie 68’); 21, A. Adli (booked, 60’)(Rayan 68’); 9, Evanilson (Unal 85’).