Level at the break, Oli Nathan headed home early in the second half from a sublime Liam stein corner, and a clever back-heel from Bloom six yards from goal caught out goalkeeper and defenders to seal victory.
NLR's David Domb told JC Sport: "Once again the boys displayed incredible character when falling behind against the run of play. They didn't panic, continued playing their normal game, and we went in at the interval level. They raised it another level in the second half, and made sure the game was beyond doubt.
I'm sure we'll face a very different L'Equipe in the league next week and give us another reminder of the good side they are, but we're finding our feet nicely in competitive football once more. We look forward to the rematch as we aim to build on a good start to the season.
NLR levelled before half time and as the second half went on, L'Equipe were tiring with only 11 men and conceded from two sloppy corners.
L'Equipe joint-manager Dan Cordell told JC Sport: "With a depleted squad of only 11 players I thought we really took the game to Norstar.
"We'll definitely be working on defending set-pieces in training this week. Overall we had our chances, their keeper made a couple great saves and on another day we would have won.
"But the league is the priority for us and I'm expecting a full squad next week against Norstar again."