Forty-four Football League places separate today's opponents, but Mowbray knows to his cost that is no guarantee of success.
In 1989, the Boro boss was skipper of the side that lost 2- 1 to Fourth Division Grimsby Town at Ayresome Park, despite being in the top-flight at the time.
Twelve months previously, he had watched non-league Sutton Town take Boro to a replay that was only settled in extra-time.
As a result, when he travels to the Pirelli Stadium today, he will be accompanied by a sense of trepidation.
It won't be an easy afternoon,
said Mowbray. The FA Cup wasn't always kind to me as a Middlesbrough player.
I can remember 1989, when we were in the top division but played at home to Grimsby, who were in Division Four. We lost and it was a really big shock.
We should have known better really because, the previous season, we'd drawn with Sutton and only beaten them in a replay after extra time. That was the narrowest of narrow escapes.
To be honest, I can't really remember much about either game. Maybe I've tried to blank them out of my mind.
Middlesbrough's recent FA Cup record features fewer upsets 2008's acrimonious quarter-final defeat to Cardiff City is probably the closest thing to a genuine shock but skipper Matthew Bates remembers an afternoon that almost ended in embarrassment in January 2006.
Boro were heavy favourites when they travelled to nonleague Nuneaton, and a routine victory looked on the cards when Gaizka Mendieta fired them into a 15th-minute lead via a direct free-kick.
They failed to kill their opponents off, though, and a replay was required after Gareth Southgate conceded a 90th-minute penalty that enabled fitness instructor Jez Murphy to score.
These sort of games are hard, said Bates. I remember the Nuneaton game really well. We gave away a penalty in the last minute, but it was one of the hardest games I've ever played in physically.
The pitch was awful, there just seemed to be mud everywhere, and the crowd was really enclosed. I suspect that'll be the case this time around.
It can be a nice change from the league because it's a different game and the pressure is maybe not quite the same. But that only applies if you win. We can't afford to go there and be complacent.
Burton's recent League Two record is poor, with Paul Peschisolido's side having won just two of their last eight league matches.
They secured a 3-1 victory over League Two leaders Chesterfield in the FA Cup second-round, however, and in defender Darren Moore boast a player with extensive top-flight experience.
They can also call on former Darlington loanee Jim Collins and ex-Tottenham trainee Jacques Maghoma, and having watched a number of their recent matches on DVD, Mowbray is taking nothing for granted.
You have to give Burton every respect, and from what I've seen they're a very wellorganised side, he said.
They have some real experience in there. I know Darren from my West Brom days, and he's a leader of men. He'll make sure they're fired up for the game.
Paul Peschisolido will as well, and they're a dangerous side. We have to go there with the right attitude and professionalism to win the game.
While Boro's position close to the foot of the Championship might have tempted Mowbray to rest players ahead of next weekend's relegation battle with Bristol City, the size of the club's injury list means wholesale changes are unlikely.
Kevin Thomson and Mikael Tavares will definitely miss out through injury, while Barry Robson is unlikely to be risked after straining his thigh.
Gary O'Neil could start after shrugging off an illness to return to full training on Thursday, while a fit-again Jonathan Franks could also be involved for the second game in a row.
We have to be a little bit careful with Jonathan because he's been out for a long time, said Mowbray.
He really needs a full reserve game under his belt, and in an ideal world he would have had that in the last two or three weeks.
I wasn't going to put him on the bench (against Norwich), but you watch him in the gym and his energy and speed make it difficult for you to ignore him.
He's one of those players with a really infectious enthusiasm, but we need to be mindful of the injury that he's had.
Barry Robson will be the guest of the Middlesbrough Official Supporters' Club at the Riverside Stadium's Hardwick Suite on Monday, January 10.
Doors open at 7pm for a 7.30pm start and fans are able to join MOSC on the night.
Source: Northern Echo
Source: Northern Echo