A John Marquis double ensured all three points for Rovers at a bitterly-cold Valley.
Rovers made one change from Tuesday's 4-1 drubbing of MK Dons in the Papa John's Trophy, with Josh Coburn replacing the injured Jordan Rossiter. Aaron Collins maintained his 100% appearance record after an injury scare to join Coburn up top, with two-goal midweek hero John Marquis on the bench.
There was an early scare for Rovers after a Rak-Sakyi header forced Belshaw into a flying one-handed save in the third minute.
The Gas goalkeeper was called into action again three minutes later as he pushed Stockley's long-range effort behind for a corner and required treatment after colliding with the post. Thankfully, the number one was deemed fine to continue.
Charlton had begun the game brightly after relieving ex-Rovers manager Ben Garner of his duties the previous week, and Belshaw had to be alert again to save Rak-Sakyi's close-range drive. Even better was to come in the 20th minute as the stopper somehow kept out Stockley's point-blank header.
However, from the resulting corner, Inniss gave the hosts a deserved lead with a well-placed header.
Individual brilliance from Evans nearly drew the Gas level in the 25th minute, beating two men and curling a shot on target that Maynard-Brewer did well to push away.
The midfielder saw yellow two minutes later after a quick free-kick went wrong and he pulled the shirt of Fraser. From their free-kick, Charlton nearly went two-up, as Blackett-Taylor escaped down the right and his dangerous cross was intercepted by the overworked Belshaw.
Sinclair showed some nice wing play in the 40th minute, but his cross was too close to the home 'keeper as the Gas looked to find a way back into the game.
Evans then let fly from distance, with Maynard-Brewer rooted to his spot; unfortunately it was just too high. Collins was upended as the half drew to a close to give the Gas a free-kick in a promising area. Evans' delivery was headed behind for a corner.
The hosts cleared, only for Coutts to be fouled to hand Rovers another chance to deliver the ball into the area; Evans drilled his cross straight at Maynard-Brewer and a disappointing half was brought to an end by referee Allison.
Luca Hoole was drafted into the action for the second period, replacing James Connolly. Coutts was booked for a late tackle as the Gas looked to exert some authority onto proceedings. Marquis was next to enter the fray, replacing McCormick, prompting a change of shape for Rovers with Sinclair sitting just behind the strikers.
Out of nothing, Marquis robbed Fraser and curled a shot into the top corner to get Rovers back on parity.
Rovers almost made it two as Maynard-Brewer was forced into a sprawling save to deny Coburn. From the corner, Thomas headed narrowly over.
Collins then fired from distance but too close to the increasingly-busy Maynard-Brewer. Marquis was desperately unlucky not to score his second after 67 minutes as Coburn's cross bounced off him with the goal gaping.
At the other end, a Charlton free header from a corner flew inches wide as the game started to become stretched. Evans then blazed over the bar from distance after the ball was punched clear.
Marquis did make it 2-1 to the Gas in the 72nd minute, as Coburn let the ball run for the striker to slot calmly beyond a helpless Maynard-Brewer to ensure all three points for Rovers who sit in ninth place at Christmas. Three points off the play-off places.
Next up for Rovers is a Boxing Day clash with Wycombe at Adams Park.
Rovers: James Belshaw, James Connolly, Lewis Gordon, Scott Sinclair, Aaron Collins, Paul Coutts (c), Lewis Gibson, Antony Evans, Luke McCormick, Bobby Thomas, Josh Coburn.
Substitutes: Jaakkola, Kilgour, Marquis, Saunders, Whelan, Gibbons, Hoole.
Charlton: Ashley Maynard-Brewer, Sean Clare, Sam Lavelle, Ryan Inniss, Steven Sessegnon, George Dobson, Jack Payne, Scott Fraser, Corey Blackett-Taylor, Jayden Stockley (c), Jesurun Rak-Sakyi
Subs: Nathan Harness, Albie Morgan, Charlie Kirk, Chuks Aneke, Miles Leaburn, Richard Chin, Zach Mitchell.
Referee: Sam Allison.
Attendance: 12,340, incl 1,339 away