Bernardini had three 3-pointers in the second half for the Quakers (4-3), who were 1 of 10 from beyond the arc in the first half and finished 7 for 18 from there.
Jeremy Hence had 15 points for the Black Knights (4-4), who lost their third straight game.
Ella Ellis hit a 3 to open the second half for Army and gave it a 31-28 lead. Penn went on a 10-0 run with Bernardini scoring half the points to take a 38-31 lead with 14:39 to play.
As Penn started to connect from the outside, the Black Knights started missing from everywhere, shooting just 29.6 percent (8 of 27) in the second half to finish at 36.5 percent (19 of 52) for the game, including 9 of 25 from 3-point range.
When Army did close within 47-41, Bernardini hit a 3 with 8:31 left and the Black Knights were never closer than seven the rest of the way. Penn's biggest lead was 66-49 on a jumper by Rob Belcore with 2:28 to go.
This was the second straight game Army scored a season-low coming off 56-54 loss to Buffalo.
This was Penn's fourth straight win and seventh of eight in the series which the Quakers lead 21-12. The schools last met in the 1999-2000 season and that game was their first since 1958-59.