Fletcher took advantage of a woeful first-half display from the visitors to hand Bournemouth a two-goal half-time lead, before reaching his personal landmark in the 57th minute.
But the giant striker owed a huge debt to team-mate Wade Elliott who created all three goals during a magnificent performance on the right wing.
Fletcher was perfectly placed to open the scoring in the fifth minute after Brentford goalkeeper Stuart Nelson failed to hold Elliott's low shot.
The second came half an hour later after Elliott delivered an inviting cross from the right byline for Fletcher to send an unstoppable diving header inside the left upright.
The forward could have completed his hat-trick in the closing stages of the first half but chose to unselfishly set-up Neil Young, only the full-back to slice his effort wide.
However, Fletcher was not to be denied and grabbed his third 13 minutes after the interval when he headed home at the far post before being mobbed by his delighted team-mates.
Bournemouth should have had the game won in the first half but suffered a setback five minutes after the restart when Isaiah Rankin reduced the deficit with a hopeful shot from the edge of the area.
Fletcher settled the home crowd's nerves with his third but Bournemouth were left clinging on for their seventh home win of the season after Rankin netted a superb individual goal from 25 yards out in the 65th minute.
There appeared little on when the striker received the ball outside the penalty area, but Rankin stepped up to curl an unstoppable shot into the top right hand corner.