The home side had to come from behind but led 3-1 thanks to Kemar Roofe's brace, which came after Liam Sercombe had equalised with a penalty.
Athough Bafetimbi Gomis pulled a goal back midway through the second half, a feature of the game was how assured United were on the ball.
Appleton, United's head coach, said: "The whole day was magnificent.
"From the number of fans we had in the Kassam Stadium, down to the performance.
"It's one thing to beat a Premier League side on your own patch, but the way we passed the ball and created chances was great.
"I said to the players before the game we don't have to play with fear.
"We all want to pit our wits against the best and we've done it in the way we've been doing it all season."
Roofe, who now has 15 goals for the season, said: "We didn't change our way, we play football similar to them and we just worked hard.
"From front to back everyone put in a shift and it paid off."
Centre back Johnny Mullins added: "There's a big smile on my face which has been there since the final whistle.
"It's a day we've thoroughly enjoyed."
- Reactions at full-time, via the FATV's Youtube channel