The Addicks, who had not scored in their previous four matches, looked set for a third straight goalless draw under new coach Riga.
But defender Dervite powered home a dramatic late header to lift Charlton out of the relegation zone and above their south London rivals Millwall on goal difference.
After Tuesday night's Championship win, Riga said: "Dorian has a good reading of the game, he understands it very well and passes it well.
"The only point with him he is sometimes he is too introverted. He needs to be more like the boss."
Dervite's first goal of the season was only Charlton's 13th at home in the league, but it could yet prove to be a very lucky one.
Bournemouth had dominated the opening half an hour but had nothing to show for it, Lewis Grabban, Steve Cook and Harry Arter all spurning opportunities.
But the second half was all Charlton and the impressive Diego Poyet twice forced fine saves out of Lee Camp before the late drama.
In the second minute of injury time Camp palmed Johnnie Jackson's free-kick over the crossbar and from the resulting corner, Dervite rose highest to nod home.
The Charlton fans, so enraged by Chris Powell's sacking and Riga's suspiciously swift appointment last week, were singing the Belgian's name at the end.
He added: "To be good with the fans I have to take points first. We will see how valuable that goal is at the end of the season.
"Of course I am happy. I knew when I arrived we would have to work hard and find solutions together and finally we found one.
"At this moment we are out of the bottom three. We deserved to win but it's only one step."
Bournemouth arrived at The Valley still with half an eye on a late play-off push but boss Eddie Howe admitted their lack of a goalscoring threat cost them.
"We were very good early on, we dominated but then we tailed off," he said.
"We didn't score when we were on top, then Charlton to be fair rolled their sleeves up and dug in. We gave away too many free-kicks and one of those cost us at the end.
"I think we defended okay but we didn't look like scoring and that's a concern."