The game was a notable one for Luke McNally, the Irish defender making his return for the Robins after being out for 608 days with an anterior cruciate ligament injury.
But his side conceded from the first attack in the eighth minute when Grant beautifully controlled Tyreece Campbell’s cross from the left before firing home left-footed for his second goal of the season.
City took charge and Charlton goalkeeper Arthur Okonkwo was fortunate to escape conceding a free-kick on the edge of his area, and perhaps a red card, when he appeared to bring down Yu Hirakawa after the Japanese forward latched on to Josh Edwards’ under-hit header.
Dom Ballard headed over for the visitors, but then won City’s penalty when he was felled by Conor Coventry for Twine to slide home on 27 minutes.
The Robins maintained the pressure and Okonkwo did well to touch away Twine’s free-kick at his right-hand post.
The second half was poor although Addicks forward Campbell twice went close in quick succession, his first effort saved by City goalkeeper Sam Tickle before he fired another over.
Charlton might have snatched all three points in the final minute but Tickle did well to touch over Harvey Knibbs’ free-kick with a strong right hand.