Danjuma bagged his third goal of the season nine minutes from time and only six minutes after his introduction as the Cherries maintained their unbeaten start to their league campaign.
City were the superior team in the first half and could have taken the lead with only four minutes played.
Wales defender Chris Mepham gave the ball away cheaply inside his own penalty area and was relieved to see Antoine Semenyo fire into the side-netting at the near post.
City carved another presentable chance from the resulting corner but Famara Diedhiou could not keep his header down.
The Robins thought they had taken the lead on the half-hour mark through Tomas Kalas' looping header from another corner only for Josh King to nod the ball away from off his own goal-line.
Bournemouth boss Tindall once again left Wales winger David Brooks watching from the stands and the Cherries badly missed his creative spark in a lacklustre opening 45 minutes.
City goalkeeper Daniel Bentley only had to get the gloves dirty once before half-time when he reacted quickly to push wide Solanke's deflected left-footed effort.
City ended the half as they started it – on the front foot – and Diedhiou was only denied by a brave block from former Robins defender Lloyd Kelly after finding space inside the 18-yard box.
Bournemouth came out with more purpose after the interval and came agonisingly close to taking the lead in the 54th minute.
Kelly raced to the byline before cutting a cross back and Solanke diverted the ball against the outside of the post with Bentley beaten.
Moments later Stanislas drilled a shot narrowly wide after turning neatly just inside the City penalty area.
In the 66th minute Lewis Cook drove a hopeful long-range effort straight into the gloves of an underworked Bentley as City continued to frustrate their former Premier League hosts.
Just when the match looked destined for a draw, super sub Danjuma popped up with the winner.
The Dutch winger skipped past City defender Zak Vyner after being played in by Solanke before calmly lifting his shot over the advancing Bentley.