Plymouth boss Tom Cleverley was relieved after taking the honours in the Devon derby as a 2-0 win over Exeter booked a Carabao Cup second-round date with Coventry.
Alex Hartridge and Bim Pepple both scored in stoppage-time at Home Park to help the Pilgrims reach the next round and meet Frank Lampard's Premier League newcomers.
Exeter substitute Ethan Sunderland was dismissed two minutes from time after receiving two yellow cards after his 65th-minute introduction.
Cleverley told BBC Sport: "I'm sure that when I put my head down tonight there'll be a real proud and pleased part of what I feel, because we've managed to overcome a lot of challenges last year as a team and prove a lot of things that we were not so good at, but the one thing that was outstanding was a derby win.
"We didn't show the best version of ourselves last year in both of them so it's nice to put a dominating performance on."
Exeter boss Matt Taylor felt the Grecians deserved more from the game.
He said: "It was a painful end. For large parts, we were connected, disciplined, solid and honest as a team without creating enough throughout the course of the game.
"Then a spell of inexperience, a couple of yellow cards in quick succession, and then it was just the amount of balls in our box from that point on.
"In terms of where the group are, that was a really honest display and we're so disappointed that we've got nothing to show for it."
