The Hornets travelled to Prenton Park for their third-round replay, with the first meeting ending in a thrilling 3-3 draw at the start of this month.
Tranmere were forced to cancel the original replay due to a waterlogged pitch, but they finally got their chance to shine when they beat the Hornets in extra-time.
The League One outfit opened the scoring through Emmanuel Monthe but Hornets youngster Kaylen Hinds grabbed an equaliser in the 68th minute.
Substitute striker Paul Mullin, who came off the bench to score the equaliser in the 3-3 draw, then went one better as he headed home with 14 minutes remaining.
Tranmere will now look forward to a clash with Manchester United on home soil this weekend, while Pearson will plan for Watford's next Premier League fixture against Everton on February 1.
Pearson made eleven changes for the trip to the north west, and he was pleased as he got the chance to assess some of the fringe members of his squad.
He told the club's official website: "We learned a lot about our young players tonight, and I thought the senior players who were involved were excellent.
"The added benefit is some of our youngsters have been introduced to men's football, and welcome to it! It was a really tough game, congratulations to Tranmere. It would have been nice to get to penalties after we got to extra time, but it wasn't to be.
"It's been a very valuable experience for us as coaching staff to have a look at some of the players who we didn't know all that much about."