In 2008 Harry Redknapp's Pompey went to Old Trafford in the quarter-finals and stunned Manchester United 1-0 on their way to lifting the trophy.
Portsmouth were, of course, a Barclays Premier League team themselves at that time, going on to finish eighth.
Administration and relegation have since taken their toll at Fratton Park, with Pompey now 17th in the npower Championship and yet again looking for new owners.
And Appleton admits a win at Stamford Bridge would be an even more impressive achievement than victory over United.
"It would be bigger than that, because a lot has happened to Portsmouth since then," he said at his pre-match press conference.
"We're in the Championship now with a small squad and a lot of players who are coming towards the end of their careers.
"But we're in good form lately and hopefully we can be one of those teams around the country celebrating a shock this weekend.
"Chelsea haven't had a fantastic first half to the season, but they had a good win at Wolves earlier this week which will have lifted them, and this is a competition they want to win.
"We just have to hope they go into the game with the attitude that they're facing a side in the bottom half of the Championship, and that we then catch them off guard."
Much of Pompey's hopes will rest on the broad shoulders of 6ft 5in Hungarian striker Marko Futacs, who has broken into the first team under Appleton.
The 21-year-old has scored twice in the last two games and is looking to cap a memorable few days with an FA Cup giantkilling.
"It's really exciting. If I'm involved then it will be the biggest game of my career," he told Pompey's official website.
"In the FA Cup there's always the chance of a shock, so of course we can go there and win the game. It will be difficult, though, because Chelsea are a very big Premier League side and we are smaller.
"But we've played really well in the last few games and if we show the same level of hard work and play to our very best then we can beat them.
"There are some brilliant players in the Chelsea side, but you can't let that affect your game.
"We have to think that we are equal on the pitch and we deserve to be playing against them."