The 19-year-old broke the deadlock after 62 minutes with a stunning strike.
Turning his marker on the left wing, Harrison raced forward and cut inside before drilling a 20-yard rocket past Josh Lillis.
After Rochdale substitute Michael Rose had equalised with a brilliant effort of his own from 25 yards, Harrison notched the winner from close range when Ryan Brunt's 84th-minute shot had been saved.
"There is a youthful enthusiasm about Ellis that you want to keep, while hoping he matures in other ways," said Ward.
"He is learning fast and has already shown he can bounce back from days when he is less effective.
"I had to ask my coaching staff the other day whether Ellis is left or right-footed because he strikes the ball so cleanly with both feet. He is a very exciting talent.
"We weren't ourselves in the first half and our goalkeeper has kept us in it, which hasn't been the case very often."