The 25-year-old had missed three games with a thigh strain but declared himself fit to face Rovers on Saturday and opened the scoring with his 32nd goal of the season.
Leeds went on to win 3-1 and Grayson highlighted Beckford's presence as a key factor behind their 10th straight success at Elland Road.
"Jermaine wanted to play so we left the decision to him," he said.
"When his name is on the teamsheet it probably puts a bit of fear into the opposition.
"Jermaine has an eye for goal but he needs good players to create the chances and Robert Snodgrass set him up for his goal with a great piece of play."