Warrington took the lead inside the first minute in controversial circumstances. Matty Regan cut the ball back from the byline and Matthew Grivosti tapped in while a Scholars player was down with a head injury.
Chasetown came back strongly and Aaron Ashford and Jack Langston were both inches off target from long range.
It was an end to end first half and Luke Duffy forced a low save from Curtis Pond before Daniel Atherton saved a curler from Joey Butlin.
The hosts almost made it 2-0 but Andy Parsons headed off the line.
Pond denied a long range Grivosti effort at the start of the second half as the visitors had to survive a sustained spell of pressure from the Yellows.
Warrington went close again as Pond raced out of his goal and Duffy fired an open goal from a wide angle into the side netting.
Pond made another top save to deny Duffy and then Chase sub Liam Kirton had a shot deflected over, denied by the offside flag.
Chase had a succession of dangerous corners and Ryan Wynter's bullet header was hooked off the line by the keeper's right hand post.
The Scholars thought they had earned a corner but the referee gave a goal kick and the Yellows broke quickly and Duffy smashed a low shot beyond the dive of Pond to seal Chasetown's fate.
Sean Williams hit the post for Warrington deep into stoppage time.
In the final seconds Scholars left back Zack Foster was sent off.