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Bobb produced a fine bit of individual skill to strike in the 80th minute as he twisted his way into the box and bent a shot into the far corner, only his second goal for the club in any competition since his £27million move from Manchester City back in January.
That was enough to give Fulham their first away win in nine attempts, a run that dated back to February, only a week after they ended their winless start to the league campaign by edging out Hull 1-0 as the pressure continues to ease on Alvaro Arbeloa.
Josh King had earlier hit the post for the visitors, who edged Coventry in just about every department to leave Frank Lampard’s side second-bottom of the table.
The hosts had only brief spells of sustained possession in Fulham’s half, but did little to trouble Bernd Leno on a frustrating afternoon which bought the CBS Arena back down to earth after their 4-1 win over Newcastle in their last home outing.