Stevenage had an 18th-minute penalty claim ignored when Mark Roberts went to ground under a challenge from Yann Kermorgant and the Addicks had a similar appeal rejected by the officials after Johnnie Jackson appeared to have been tugged back by Joel Byrom.
Wright-Phillips should have put the leaders in front in the 36th minute when he was picked out by Kermorgant's pass, but his volley ended up on the roof of the net.
Luke Freeman almost gave Stevenage a first-half stoppage time advantage, but he fired his shot into the ground at the back post after connecting with Stacy Long's cross.
Charlton broke the deadlock within four minutes of the restart with Morrison's stunning shot from 20 yards that flew past Stevenage goalkeeper Chris Day for the defender's fifth goal of the season.
And the lead was doubled in the 64th minute as Wright-Phillips shook off Jon Ashton and ran into the box before firing past Day, with Stevenage's Ronnie Henry possibly getting the last touch on the goalline.