The Addicks, who had not scored in their previous four matches, looked set for a third straight goalless draw under new coach Jose Riga.
But defender Dervite powered home a dramatic header at The Valley on Tuesday night to send Charlton above their south London rivals Millwall on goal difference.
It was only their 13th home league goal this season, but it could prove to be a lucky one come the end of the season.
Yet the opening stages were dominated by a Bournemouth side who still have half an an eye on a late play-off charge.
Marc Pugh set the tone for the visitors when he fired narrowly over with just 20 seconds on the clock.
Addicks goalkeeper Ben Hamer had to make saves from Steve Cook and Harry Arter while Lewis Grabban's shot from a well-worked corner was too high.
Charlton eventually settled and Danny Green was put through by a neat ball from Diego Poyet but Lee Camp smothered his angled drive at the second attempt.
Green then inadvertently close to breaking Charlton's duck when his cross crashed against the outside of Camp's near post.
Riga sent on new loan signing Jonathan Obika for youngster Callum Harriott with five minutes of the first half still to play and the striker was immediately in the thick of the action, forcing Camp into another smart save with a drive from the edge of the area.
After the break industrious midfielder Poyet, the son of Sunderland boss Gus, almost broke the deadlock but his lob landed on the roof of the goal.
Riga threw on Marvin Sordell to join Obika and Simon Church in Charlton's attack while Yann Kermorgant, the popular striker controversially sold by Valley owner Roland Duchatelet to make way for a raft of his own signings, came on for Bournemouth.
But it was Charlton who were pushing for the winner, and they came close to when Church, who looked offside, was thwarted by the outstretched arm of Camp before Johnnie Jackson's follow-up was blocked.
Camp saved again from Poyet and then tipped Jackson's free-kick over the top.
But from the corner, Dervite met Jackson's cross with an unstoppable header to seal a dramatic and long overdue win for the hosts.