Briggs found the bottom corner with a tidy finish midway through the opening period, while the visitors were unable to take the chances that came their way.
The left-back put his side's chances of progressing to the second round when he received a red card for a second yellow after the interval, but the hosts did just enough to keep Wycombe at bay.
Gareth Ainsworth named an unchanged side from the excellent 2-0 win at Newport on Saturday, while his counterpart Ian Holloway shuffled the pack with seven changes, handing debuts to four summer signings - perhaps with one eye on Saturday’s trip to London rivals Fulham.
It was the visitors who created the first chance and home keeper David Forde needed to be alert to parry away a superb volley from Paul Hayes inside seven minutes, meeting Sido Jombati’s cross with a clean connection from 15 yards out.
Lions striker Lee Gregory had two sights of goal within a minute on the quarter-hour mark, firstly stealing the ball off Alfie Mawson before being pressured away from danger, and then chesting the ball down from Magaye Gueye’s well-placed cross but seeing the ball evade him into Matt Ingram’s arms.
Wycombe were more than holding their own in the game but fell behind on 27 minutes after a good spell of possession from the home side. The movement of the left winger Magaye Gueye distracted the visitors’ defensive shape and Matthew Briggs stole in unmarked to collect a loose ball and find the bottom corner to cap his debut in style, receiving a yellow card for removing his shirt in celebration.
Ainsworth’s men responded well and forced a corner after intelligent play from Hayes and Max Kretzschmar, while Alfie Mawson was close to making contact from the delivery as the ball flew across the six-yard box.
They were even closer moments later when Matt McClure held the ball up superbly in the area and laid it off to the advancing Sido Jombati, whose low shot seemed destined for the bottom corner before Forde was equal to it with a brilliant one-handed save.
Wanderers continued to pose the bigger attacking threat after the break and looked to capitalise on Millwall’s assured but often careless approach to possession.
And then the visitors were handed a massive boost when goalscorer Briggs received his second yellow card for a late tackle on Jombati, having already been booked for his celebration.
Moments later, Lee Gregory forced a low save from Ingram before the keeper had to be alert to nick the ball off the toes of substitute Fred Onyedinma, who had raced clear into the area.
Chances began to dry up once the tempo settled again, although Peter Murphy did meet an inviting Paris Cowan-Hall cross but sent his header wide of the post on 72 minutes.
Two minutes later, Hayes flicked the ball goalwards after a clever cross from Cowan-Hall but the ball struck the back of Byron Webster and went behind for a corner.
Cowan-Hall almost forced a leveller on 82 minutes when Hayes’ low cross came off Jimmy Abdou and struck the winger’s body, but the contact wasn’t enough to force the ball over the line.
Gareth Ainsworth introduced Matt Bloomfield and Steven Craig as part of a reshuffle to a 3-4-3 formation, and the striker should have hit the target with a glancing header from Cowan-Hall’s cross but the ball bounced wide.
Five minutes of stoppage time came and went as the Blues were unable to find the crucial equaliser and must turn their attentions to the first home game of the new campaign when Carlisle United roll into town on Saturday.
Wycombe: Ingram, Jombati, Jacobson, Mawson (Craig 83), Pierre, Cowan-Hall, Murphy, Kretzschmar (Bloomfield 83), Wood, McClure (Holloway 72), Hayes (c).
Unused subs: Richardson, Rowe, Bloomfield, Walker, Morias, Craig.
Millwall: Forde, Dunne, Briggs, Shittu, Webster, Wright, Abdou, MacDonald (Powell 62), Gueye (Oyedinma 47), Easter (Siafa 84), Gregory.
Unused subs: Bywater, O’Brien, Goodman, Marquis.
Ref: Andy D’Urso.