Briggs was one of four summer signings to make their first starts for The Lions as manager Holloway made seven changes in all from the team that started against Leeds United on Saturday.
Briggs, Magaye Gueye, Byron Webster and Lee Gregory all came into the team, whilst the subs bench consisted of six Academy graduates - Fred Onyedinma, Josh Siafa, Aiden O'Brien, Jack Powell, Jake Goodman and John Marquis - plus goalkeeper Stephen Bywater.
It was the first time since an FA Cup game at Wolves in January 2005 that outfield players on Millwall's bench consisted entirely of homegrown talent, an indication that the immense work of the Academy coaching staff is really starting to bear fruit.
For Wycombe, Tuesday night's team was the same that opened their League Two account with an excellent 2-0 win at Newport County at the weekend, as boss Gareth Ainsworth named an unchanged side.
Although the official attendance was around one fifth of the 16,000 that packed The Den on Saturday, credit to those who did turn out to support the boys in blue as The Lions extended their unbeaten run in League and Cup competitions to 10 games.
However it was not all plain sailing for the home side who were pushed all the way by a determined Wycombe side who, in the first half, shaded possession and chances, but found themselves trailing by Briggs' goal at the break.
It took a stunning save from Lions keeper David Forde to acrobatically tip Paul Hayes thunderous volley away on seven minutes and then Paris Cowan-Hall headed wide of the mark as Wycombe threatened once more.
The home side produced their best chance of the opening exchanges just before the quarter-hour mark when a delightful slide-rule pass from Gueye picked out Gregory, but the latter just couldn't get the ball under control and keeper Matt Ingram raced off his line to collect.
At the other end Sam Wood's left shot shot was comfortably collected by Forde but moments later the deadlock was broken on 27 minutes - and what a super finish it was by Briggs, who was played in by Scott McDonald and fired the ball beyond the reach of Ingram. It was Briggs' first goal since April 2013 and his celebration of removing his shirt earned him what proved to be a costly first booking.
There was a slight defensive reshuffle made soon after with skipper Alan Dunne moving to centre half alongside Danny Shittu in a straight swap that saw Webster slot in at right-back.
Wycombe kept plugging away in the torrential rain trying to find a way through, and it took another smart stop from Forde to deny Sido Jombati an equaliser seven minutes before the break, diving low to his right to push the full-back's stinging shot away for a corner.
That proved to be the visitor's best chance of the half and it was Millwall who went in one goal to the good.
Forward Gueye was replaced by Onyedinma at the start of the second-half, but within 13 minutes of the restart Millwall found themselves a man down when Briggs received a second yellow card for a clumsy tackle on Jombati.
The Lions had a penalty appeal turned down barely 60 seconds later when Onyedinma jinked his way into the area and went down under a challenge from keeper Ingram as he prepared to shoot, but referee Andy D'Urso waved play on.
Midfielder Powell entered the fray for his senior debut on 63 minutes, replacing McDonald as the 10 men of Millwall regrouped and it was infact The Lions who looked the more likely to score again, despite their numerical disadvantage.
It took a fine last-ditch tackle by Jobati to nick the ball off the toes of Gregory as he latched onto Josh Wright's through ball whilst Webster headed wide and then Gregory sent a sweet 20-yarder a foot over the bar as Ollie's men took the game to the Chairboys.
Millwall introduced what proved to be debutant number six of the night when Josh Siafa came on for the last five minutes and The Lions dug in with one last big concerted effort to see out the remainder of the game and book their place in the Second Round.
Millwall: Forde, Dunne, Shittu, Webster, Briggs: Abdou, Wright; Easter (Siafa, 85mins), McDonald (Powell, 63mins), Gueye (Onyedinma, 46mins); Gregory. Subs not used: Bywater, O'Brien, Goodman, Marquis.
Booking: Briggs (27mins)
Sending off: Briggs (58mins)
Scorer: Briggs (27mins)
Wycombe Wanderers: Ingram, Jombati, Jacobson, Pierre, Mawson (Craig, 82mins), Murphy, Kretzschmar (Bloomfield, 82mins), Wood (Holloway, 72mins), Cowan-Hall, Hayes, McClure. Subs not used: Richardson, Rowe, Walker, Morias.
Booking: Cowan-Hall (88mins)
Ref: A D'Urso
Att: 3,403 (342)