Burch won 19-25 and 24-26 over the Lady Wolves, who were playing their final match on their home court.
The Lady Bulldogs won the second set on Ashley Farley's spike.
Prior to the game with Williamson, Burch fell to Tug Valley, 17-25 and 13-25.
"We played well against Williamson in the first set, but, we relaxed in the second set and had to dig our way out," Burch Coach Jan Cisco said.
Williamson also fell twice to Tug Valley.
"They're finally coming into their own," Williamson Coach Tondra Elkins said. "We should make a good showing in the sectional. Every player played well."
Across the county, the Matewan Lady Tigers beat the Regional Christian School Eagles, 3-0.
The Lady Tigers were also playing their final game at home.
They beat RCS, 25-9 on a Whitney Horton ace and then beat the Eagles, 25-17.
Earlier in the evening, Matewan beat RCS 25-17 and 25-11.
RCS coach Brenda Roberts said her team is tired from playing a grueling schedule.
"Jessica Floyd and Brooke Mounts played very well," Roberts said.
Clay Moore said his team played well in one set and bad in the second.
"That's the way we've been playing," Moore said. "We shut down and it takes time to get our engines started back up."
Matewan plays tonight at Gilbert, while Burch returns to action tomorrow at Logan.
RCS plays next week in their Christian school state tournament.
Williamson plays in the sectional tournament on Tuesday in Gilbert.