Defender Briggs gave the Lions the lead midway through the first half with a low strike, but was booked for his celebration.
That almost proved costly just before the hour when Briggs was shown a second yellow for a foul on Sido Jombati.
But the Championship side held on as Matt Bloomfield headed wide late on for League Two Wycombe.
Wycombe boss Gareth Ainsworth told BBC Three Counties Radio:
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"Hopefully we've gained a bit of respect form the Championship side tonight.
"I thought we deserved something from the game.
"We've got to build slowly at this club, but the signs are still there.
"We've got a big job to do, on and off the pitch last season wasn't good enough, this season is hopefully a turn around from that."
Debutant Matthew Briggs scored and was sent off as Millwall edged past Wycombe to reach the League Cup second round.