Bradley Wright-Phillips had the first opportunity after 14 minutes of Monday's League One clash at The Valley when he curled his cross-cum-shot wide of the left-hand post.
Morrison headed the hosts in front in the 31st minute when he bravely got ahead of onrushing goalkeeper Richard Lee to net his third goal of the season.
Leon Cort put a free header wide of Lee's left-hand post in first-half stoppage time following a cross from the right by Danny Green. Charlton captain Johnnie Jackson could have doubled their lead soon after the restart when his header in the six-yard box bounced off the post.
The best opportunity for Brentford came just before the hour mark when central midfielder Marcus Bean fired wide from 10 yards out. Sam Saunders blasted a free-kick over the crossbar with 12 minutes to go for the visitors.
Substitute Scott Wagstaff stretched but put his effort over the bar after 83 minutes before the game was put beyond doubt in the 90th minute when Green turned in the box and slotted home his second goal of the season.