Trailing to a 28th-minute goal from Jay Rodriguez, Town proceeded to dominate the second half in front of their raucous sell-out contingent of 2,300 away fans.
They got their just rewards when Josh Koroma levelled 13 minutes from time at the far post following a deadly cross from Sorba Thomas, who made a huge impact when he came on from the bench.
It was Koroma's first goal in 18 matches since September
Town pushed for victory against a leggy Burnley side and secured their passage into round four thanks to another assist from Thomas, whose assist count is now into double figures.
The beneficary was Matty Pearson, with the former Blackburn Rovers academy and Accrington defender heading home Thomas's corner for a richly deserved win for Town at the venue where their glorious Cup campaign of 1921-22 began a century ago.
While Pearson, Thomas and Koroma were afforded kudos, it was a team effort from Town with the likes of Jonny Russell and Josh Ruffels also impressing in their first starts for the club.
The victory extended the club's unbeaten sequence to seven matches on an afternoon when Australian keeper Nicholas Bilokapic was handed a surprise debut after Ryan Schofield came off injured close to half-time.
On Thomas's stellar contribution and Koroma's precious goal, Corberan said: "It was important to have his contribution and I want him to keep pushing himself to keep doing that. Every player needs to go to the pitch with a lot of self-demanding.
"When a young player is doing well we need to manage it well and help the player to put his best on the pitch."
"Koroma was more brave and aggressive and we know with his game that he needed recovered his aggressiveness because he provides balance to our attack.
"I watched a team from the beginning with a lot of personality. It is true in the first half that the game was more balanced and there were a couple of aspects that we did not manage well.
"But in the second half, the team were more brave and adapted and caused a lot of problems and I was watching a team who showed a lot of determination to go for the win. All of the players competed well."
Meanwhie, Corberan confirmed that Levi Colwill missed the game with a minor knee problem, with the club awaiting to see the extent of the injury sustained by Schofield, who made his first appearance since mid-August in place of Lee Nicholls.
Town's number one missed the game through illness, but it was not Covid-related.
Corberan added: "He only has a small problem in the knee.
"He hurt his shoulder and could not continue playing and we don't know if it is going to be a serious injury or less. We are waiting for the news."
On Bilokapic's promotion, he added:"He's been on the bench many times and we know he is a good goalkeeper. Today was a big day for him and a big day for me and for the academy for a young player to come through into the first team."