Goals from Evanilson, Rayan and Álvaro Rodríguez secured a second consecutive league-phase victory for the Cherries at the Vitality Stadium, giving head coach Marco Rose a welcome boost after a difficult start to their Premier League campaign.
The result also maintained Bournemouth’s perfect record in the competition after their opening-day victory away to Real Sociedad.
Evanilson opens the scoring with stunning header
Bournemouth dominated much of the opening period and created several opportunities before finally breaking the deadlock in the 43rd minute.
Captain Adam Smith delivered a cross into the penalty area, and Evanilson produced a superb looping header from distance to beat Sturm Graz goalkeeper Daniil Khudyakov.
The goal was a historic moment for Bournemouth, as Evanilson became the first player to score a European goal at the Vitality Stadium.
The hosts had previously thought they had scored when the ball entered the net following a corner, but the effort was ruled out for a handball by Bafodé Diakité.
Marcus Tavernier also struck the post as Bournemouth continued to threaten before half-time.
Sturm Graz threaten before Rayan strikes
Sturm Graz returned from the break with greater attacking intent and came close to equalising shortly after the hour mark.
Jürgen Heil struck the woodwork with a powerful effort, and Jacob-Peter Hödl’s follow-up was denied by Bournemouth goalkeeper Djordje Petrović, who produced an important save to preserve his side’s lead.
The Austrian visitors continued to push forward, but Bournemouth’s substitutions helped restore their control of the contest.
Rayan, Justin Kluivert and Ryan Christie were introduced in the 70th minute, adding fresh energy to the home side.
Six minutes later, Rayan doubled Bournemouth’s advantage. After Khudyakov failed to deal cleanly with a corner, the Brazilian collected the loose ball and fired a low shot through the goalkeeper’s attempted save to make it 2-0.
Rodríguez seals comfortable victory from the penalty spot
Bournemouth added a third goal in stoppage time after James Hill was fouled inside the penalty area by Jon Gorenc Stanković.
Álvaro Rodríguez stepped up in the 92nd minute and confidently converted the penalty, scoring his first goal for the club and completing a memorable European night.
The late strike ensured Bournemouth finished with a clean sheet and a three-goal winning margin.
Rose calls for consistency after historic night
The victory represented a significant milestone for Bournemouth, whose rise from the lower divisions of English football to European competition has been remarkable.
The Cherries had endured a difficult domestic spell, including a 5-1 defeat to Chelsea, but their European performances offered encouragement ahead of their next Premier League fixture.
Rose praised his players’ attitude, effort and defensive discipline, while stressing that they must reproduce the performance consistently.
Bournemouth’s captain, Smith, also welcomed the result, describing the occasion as long-awaited and praising Evanilson’s finishing.
Bournemouth turn attention to AC Milan
The victory lifted Bournemouth to fifth in the Europa League league-phase standings, with six points from their opening two matches.
The English side will next host AC Milan on Thursday, 22 October, in another significant European fixture at the Vitality Stadium.
Before then, Bournemouth are scheduled to return to Premier League action against Sunderland on Sunday, 18 October, hoping to carry their European confidence into domestic football.
For Sturm Graz, the defeat leaves them searching for their first league-phase victory after opening their campaign with a goalless draw against Rennes.