Jordan Rhodes's 99th career league goal has given Blackburn Rovers a 1-0 half-time lead at Ewood Park.
It was the away side who made the brighter start and came close to taking the lead in the seventh minute, when Steven Davies's 25-yard free kick skimmed the roof of the net.
However the home side responded with a free kick, which Morten Gamst Pedersen bounced off the top of the crossbar.
Rovers did take the lead just short of the half-hour mark, when Rhodes slammed home a left-footed shot following Pedersen's cross into the box.
Bristol almost found an equaliser just before the break, but Davies could only graze the outside of the post after being played in by Sam Baldock.
