Mark Duffy's late free-kick condemned the Glovers to an 11th Sky Bet Championship defeat of the season and secured a first victory in five matches for Doncaster.
The visitors failed to make their numerical advantage pay as 10-man Rovers ran out 2-1 winners at the Keepmoat Stadium on Friday night.
Furman's early goal had put the home side ahead before Byron Webster equalised against his former club on the stroke of half-time.
Furman was then sent off for a second booking, but Duffy's first goal for Dickov's side was enough to leave Yeovil rooted to the foot of the table.
"It was a fantastic result but a scrappy performance from us" said Dickov, whose side move five points clear of the relegation zone.
"When we got the goal I thought 'we can go on and get a couple here', but we seemed to lose the tempo of the game a little bit and the two banks of four dropped too deep. You can't switch on and off in games.
"The players have got to get a lot of credit because going down to 10 men at 1-1 the tendency is to sit back and take the point.
"I asked them what was wrong at half-time. It looked as if we weren't enjoying passing the ball so I asked them to up it."
- Sports & Recreation
- Mark Duffy