We were in control throughout but Brighton defended resolutely until Erik - off the bench at half-time - exchanged passes with Roberto Soldado before firing home for 1-0 on 54 minutes.
Twenty minutes later Andros Townsend crossed from the byline, Roberto’s shot was saved but Harry got to the loose ball first to slot home his eighth goal in seven cup matches so far this term.
The win set-up a quarter-final tie against Newcastle at the Lane on the week commencing December 15.
“It was a tough game,” said Harry. “Brighton sat back and soaked up the pressure but we knew if we kept the ball and kept playing that the chances would come, we’d take one and we’d be able to build on it and that’s what happened.
“As soon we scored that first goal it pushed them back, we got the momentum and we managed to get a second."
Harry bagged his first senior hat-trick against Asteras Tripolis last week and was back on the scoresheet again.
“These are the games I want to score in, getting out there and scoring goals, especially in front a crowd like that - they were great again.”