Kenny Jackett's Lions opened the scoring on Tuesday night through Neil Harris after 26 minutes before Ben Strevens scored his first goal for Wycombe with 15 minutes remaining.
But Dunne came off the bench to secure Millwall a spot in the second round.
Millwall started brightly and Kevin Lisbie slipped behind the Wycombe defence after 19 minutes only to see his shot come back off the post.
The visitors made their early dominance count when Nikki Bull palmed Danny Schofield's 20-yard shot into the path of Harris, who coolly slotted home.
But Wycombe, vastly improved in the second half, were not to be denied and Matt Phillips broke free down the right before driving into the box and teeing up Strevens to sidefoot home.
Both sides went close late on in search of a winner before substitute Dunne slammed home from close range in the 105th minute after being picked out by John Marquis.