With a limited but vociferous crowd inside the Vitality Stadium, the south coast club struck in the 55th minute when Dutchman Danjuma was slid in by David Brooks before composing himself to find the back of the net.
Brentford, beaten in last year's playoff final by Fulham after squandering a chance to gain automatic promotion, searched for an equaliser and should have grabbed one when forward Bryan Mbeumo somehow failed to convert Christian Norgaard's low cross. Third-placed Brentford had been the form team ahead of the playoffs with four successive league wins. Bournemouth, who finished sixth, lost their last three of the season.
But Brentford now face a nervous second leg at their own stadium if they are to maintain their hopes of a return to the top flight for the first time since 1947. Bournemouth are looking to bounce back at the first opportunity after being relegated from the Premier League last season after a five-season stay.
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