Cameron Jones paced Pennsbury with 17 points, including five three-pointers. Fellow junior Derrick Woods contributed 10 points and four blocks.
Chester (22-5) will open the state tournament next Saturday at a neutral site and time to be determined, vs. Carlisle, District 3's seventh-place qualifier.
Pennsbury (21-4) will begin state-tournament action next Saturday against Wilson, District 3's fifth-place finisher.
Down by 47-40 early in the fourth quarter, the Clippers, who are ranked No. 6 in Southeastern Pennsylvania by The Inquirer, trimmed the gap to two on Johnson's three-point play and Sturdivant's follow.
With 3 minutes, 15 seconds to go, after Falcons junior guard Mekhi Bryant fouled out, Chester reserve Brewster Ward sank two free throws to make it 47-all.
The Clippers took their first lead since 1-0 when Keyonte Watkins buried a right-wing trey, making it 50-47, with 2:11 to go.
Pennsbury, held to two points in the first 7:32 of the fourth quarter, closed to within 50-49 on Jones' layup with 0:28 left. Five seconds later, after making a steal, Watkins hit the second of two free throws.
From the line, Johnson bumped Chester's lead to 52-49 with 10.2 seconds to go. After the Falcons hurried the ball up the court, back-to-back three-point tries by Jones and Steve Ciotti were off the mark.
Hitting seven three-pointers, including four from Jones and a pair from Nigel Johnson, Pennsbury took a 31-23 advantage into halftime.
Early in the second quarter, Woods' inside basket put the Falcons in front, 18-5, and brought their orange-clad faithful to their feet in the upper deck. Soon after, Jones' three made it 21-9.
Down by 12, Chester responded with an 11-0 spurt capped by Khaleeq Campbell's trey from the left corner and Mahir Johnson's running bank shot.
Pennsbury closed the half with a 10-3 burst that started with Johnson's three-pointer and ended, as time expired, with another Johnson heave.
Pennsbury 16 15 14 4 – 49
Chester 5 18 16 13 – 52
P: Steve Ciotti 4, Mekhi Bryant 5, Derrick Woods 10, Cameron Jones 17, Nigel Johnson 9, Walter Allen 3, Jimmy Flagg 1.
C: Khaleeq Campbell 6, Conrad Chambers 9, Keyonte Watkins 4, Tyrell Sturdivant 17, Mahir Johnson 10, Brewster Ward 6.