Max Woltman opened the scoring with his 13th goal of the season and James Norris doubled the lead from the penalty spot.
Mateusz Musialowski then scored a goal he will never forget in front of the Kop to make it 3-0, and although the Gunners pulled a goal back, the young Reds held off a stern challenge to set up a trip to Ipswich Town in the last four.
Reflecting on the game, U18s boss Bridge-Wilkinson admitted he was delighted with the outcome and certain parts of the performance.
“[There were] definitely two parts to the game,” he said.