Witherspoon produced 13 of his season-high 19 points in the second half, grabbed five rebounds, dished two assists, and made a steal.
"I just played with confidence," the 6-foot, 188-pounder said. "If I have confidence in myself, I don't feel anyone can stop me."
Witherspoon, who lives in Olney, shot 5 for 9 from the field (1 for 1 from three-point range) and 8 for 10 from the line.
"Nobody has practiced harder," La Salle coach Joe Dempsey said. "He has been working on his perimeter game and his foul shooting, and it showed today."
The Explorers (20-6) led, 51-38, early in the fourth quarter. The Pioneers, sparked by junior forward Martin Dorsey, trimmed the gap to 58-56 on Zach Yonda's three-pointer with 2 minutes, 22 seconds to play.
"I think we lost our focus," Witherspoon said. "We weren't aggressive on offense or defense, and that allowed them to get some momentum."
It was Witherspoon's three-point play, on a left-side drive with a minute remaining, that gave La Salle a 61-56 lead and all but clinched a berth in the second round of states.
"We really needed a basket," Witherspoon said. "I couldn't let my team down."
In the second round Wednesday, at a neutral site and time to be determined, La Salle will face District 3 runner-up Cedar Crest, which defeated Spring-Ford.
Against Conestoga, which committed 10 turnovers in the middle two quarters, 6-7 forward Dave Krmpotich recorded 18 points, point guard Najee Walls netted 11, and reserve guard Dan Corr added two threes, three rebounds, and three assists.
Dorsey ignited the Pioneers (24-6) with 22 points, including 12 in the fourth quarter, and 10 boards. Guards Darryl Caldwell (13) and Zach Yonda (10) were also double-digit scorers.
La Salle 11 18 18 17 - 64
Conestoga 8 14 12 24 - 58
LS: Najee Walls 11, Chuck Champion 3, Dave Krmpotich 18, Jalen Herdsman 4, Shawn Witherspoon 19, Sean Greenberg 3, Dan Corr 6.
C: Darryl Caldwell 13, Zach Yonda 10, Dan Vila 4, Andrew Diehl 9, Martin Dorsey 22.