Danjuma fired the winner 16 minutes into the second half to end the Cherries' two-match losing streak.
Bournemouth's victory was marred by a stoppage-time brawl during which Watford striker Joao Pedro and Bournemouth midfielder Jack Wilshere were both sent off.
Elsewhere, Nigel Pearson enjoyed a winning start as Bristol City manager as the visitors came from behind to win 3-1 at Swansea City.
Former Leicester City boss Pearson saw his new team fall behind in south Wales when Kasey Palmer's handball allowed Andre Ayew to fire the hosts into a deserved lead from the penalty spot.
But Nahki Wells equalised before Palmer looped a corner all the way over goalkeeper Freddie Woodman's head.
Antoine Semenyo sealed the points for City to dent fourth-placed Swansea's promotion hopes.
Second-placed Brentford fought back to boost their automatic promotion push with a 2-1 win over Stoke City.
Vitaly Janelt levelled in the 56th minute after Jacob Brown had put the visitors ahead early on and Ivan Toney's 25th goal of the season gave Brentford a second successive victory.
Brentford is three points ahead of third-placed Watford in the race to reach the Premier League.
Luton Town stunned struggling Sheffield Wednesday with a 3-2 victory at Kenilworth Road.
The Hatters were trailing 2-0 at half-time to Josh Windass's double.
But Luton was level after just 15 minutes of the second period, with Kal Naismith and Ryan Tunnicliffe scoring, before Elijah Adebayo then headed home a dramatic late winner.
Birmingham City scored two late goals in three minutes to earn its first home win in 13 games as it came from behind to beat Queens Park Rangers 2-1 at St Andrew's.
Paddy McNair's late equaliser for Middlesbrough in a 1-1 draw at The Riverside prevented Mick McCarthy's Cardiff City from winning a seventh straight match.
Fifth-placed Reading won 1-0 at third-bottom Rotherham United, which has lost its past five games.
Matty James's first goal since 2017 earned 10-man Coventry City a 1-1 draw at Blackburn Rovers.
Barnsley won its fifth league game in a row, beating Millwall 2-1, while Preston North End defeated Huddersfield Town 3-0.