Drew Brown doubled and Biscuit Arnaud reached on a error to start the Blue Jay surge in the bottom of the first inning.
Austin LaFleur hit a sacrifice to plate Brown, while Arnaud scored on a single to left field by Christian Walker.
The Pioneers tied the game 2-2 in the top of the second when Wyatt Sullivan hit a two-run double to right field.
Notre Dame added a run in the top of the third, but the Blue Jays tied the game in the bottom of the frame when Perry Pitre walked and scored on a double by Brown.
The Pios exploded for four runs in the top of the fourth inning to push ahead, 7-3.
Sullivan, Jacque Thibodeaux and Jeff Daigle accounted for all the RBI in the frame.
St. Edmund closed the gap to 7-4 in the bottom of the inning when Andrew Hunt singled and scored on a passed ball.
Notre Dame added three more runs in the top of the sixth, sparked by another RBI by Thibodeaux.
St. Edmund closed the gap to 10-5 in the bottom of the sixth when Arnaud reached on a fielder’s choice and scored on a passed ball.
The Pios pushed across their final run in the top of the seventh when Sullivan singled and scored on a hit by Thibodeaux.
Brown led St. Edmund with a 3-for-3 performance inlcuding a RBI, a double and a run scored.
St. Edmund continues Summer League action at 5:30 p.m. on Tuesday when Opelousas Catholic visits North Park.