Galloway netted 20 his points in the second half to spearhead a rally that saw the Explorers (14-5, 4-2 A-10) follow up Wednesday's last-second win over No. 9 Butler with another upset against a ranked foe.
It was the first time La Salle has accomplished such a feat since 1952.
Tyreek Duren added 16 points as the Explorers overcame an eight-point deficit with under 15 minutes remaining.
Juvonte Reddic had 22 points and 10 rebounds for VCU (16-5, 4-2), which dropped its second straight.