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Charlton got their season off to a winning start despite having Lee Novak sent off inside seven minutes on Saturday.
The Addicks bagged all three points after a fine defensive display, scoring in the first half through defender Patrick Bauer.
Despite having a numerical disadvantage for so long, it was no more than the home side deserved on the opening day of the League 1 season.
Charlton boss Karl Robinson welcomed back Jason Pearce following a shoulder injury but Josh Magennis (knee) missed out.
Probably the quickest red card of the season came after just seven minutes.
Trying to win the ball back high up the pitch, Charlton striker Novak went in two-footed on Rovers' Stuart Sinclair.
He may have won the ball first but the challenge gave referee Chris Sarginson little option but to brandish the red card.
Sinclair quickly reverted to right-back after Rovers lost James Clarke to injury while Liam Sercombe was cautioned for a trip on Tariqe Fosu.
Charlton took the lead on 38 minutes when Ricky Holmes won a free-kick on the left-wing. Holmes delivered the cross and keeper Adam Smith was unable to keep out Bauer's header.
Rovers hardly threatened in the first half as Charlton's 10 men kept their shape well with Ahmed Kashi impressing as the holding midfielder in front of the back four.
The visitors picked up the pace at the start of the second half. A couple of wayward shots were followed by the first serious piece of action for Charlton keeper Ben Amos, who beat away Liam Sercombe's low drive.
At the other end, Ricky Holmes' free-kick was comfortably saved but on the break both Holmes and Fosu proved good outlets for Charlton.
Rovers as an attacking force failed to create enough chances against the 10 men but Charlton more than deserved to hold on for all three points.
Charlton: Amos, Solly, Bauer, Pearce, Dasilva, Kashi, Forster-Caskey, Holmes (Crofts 90mins), Fosu (Ahearne-Grant 84mins), Clarke (Watt 70mins), Novak. Subs not used: Phillips, Konsa, Sarr, Reeves.
Rovers: Smith, J Clarke (Nichols 15mins), Lockyer, Broadbent, Brown, Lines, Sercombe, O Clarke (Broom 65mins), Bodin, Harrison (Gaffney 65mins), Sinclair. Subs not used: Slocombe, Burn, Bola, Partington.
Attendance: 12,968 (2,174 away).