Danjuma rifled home with a blistering curling shot six minutes from time after Blackburn had twice come from behind at the Vitality Stadium.
It was Tindall's first competitive match at the helm since replacing long-serving Eddie Howe following Bournemouth's relegation from the Premier League last season.
Stacey brought a poor game to life with a stunning opening goal – his first in Bournemouth colours – in the 25th minute.
There looked little danger when Junior Stanislas rolled the ball into Stacey's path but the wing-back's 25-yard thunderbolt flew in off the inside of the post.
Bournemouth looked comfortable with their lead until Johnson's speculative 35-yard shot squirmed through the gloves of the hapless Mark Travers to make it 1-1 three minutes before half-time.
The south-coast side were back in front only eight minutes after the re-start courtesy of Lerma's first goal in seven months.
Stacey rolled the ball into the feet of Dominic Solanke, who turned neatly into space and could have shot himself before selflessly teeing up Lerma to side-foot into the corner from the edge of the box.
Blackburn's debutant goalkeeper Thomas Kaminski made a stunning save to deny Bournemouth a third goal by keeping out Solanke's close-range effort from Danjuma's cut-back.
Just when it appeared Tindall's reign would get off to a disappointing start, Danjuma picked up the ball on the edge of the penalty area before curling an unstoppable right-foot shot into the top corner.