A deflected Marcus Tavernier strike was enough to earn Bournemouth their first Premier League win of the season and condemn 10-man Wolves to a second straight defeat.
Both teams were hoping to bounce back from opening-day losses but, other than an early Marshall Munetsi chance, the Cherries were far more composed, organised and dangerous in the opening stages and deservedly took an early lead.
Jean-Ricner Bellegarde's poor pass on the edge of Wolves' area allowed Antoine Semenyo to pick out Tavernier, whose low shot took a wicked deflection off Emmanuel Agbadou before ending up in the net via the underside of the crossbar.
Semenyo rattled the bar from David Brooks' cross as Bournemouth sought to press home their advantage while at the other end Djordje Petrovic was forced into a smart one-handed save from Jorgen Strand Larsen's shot.
But the visitors' hopes of clawing their way back into the contest suffered a major blow when Toti Gomes was shown a straight red card for bringing down Cherries striker Evanilson as last man, leaving his team a man light for the majority of the second half.
Jose Sa made a fine save from Tyler Adams' long-range drive to keep Wolves in the game but Bournemouth saw out the final stages to claim a deserved three points.
