Charlton were reduced to 10 men in the 71st minute after Dailly saw red for an elbow on Sam Williams, but the visitors also went a man down 14 minutes later when Paul Huntington fouled Akpo Sodje in the area.
Johnnie Jackson converted the subsequent penalty to clinch Charlton the points. He gave his side an 11th-minute lead, which was cancelled out by Andrew Williams.
Therry Racon put Charlton back in front and Gary Doherty's own goal hauled Yeovil level again before Jackson's late spot kick.
Charlton assistant-manager Tim Breacker said: "We're going to have a look at Christian Dailly's red card on the video. Christian is not the sort who would lead on an elbow. He's quite adamant it was his head that he caught.
"It was a good result for us, but obviously the performance wasn't as great as we would have liked. Maybe it's a sign of a good team that when things aren't quite flowing, as they did last week at Peterborough, that we still pick up the three points."
Source: PA
Source: PA