The afternoon did not get off to the best of starts as the visitors led through Callum Wilson's early strike, but goals from captain Billy Sharp and substitute John Lundstram turned the match on its head as it finished 2-1.
The win moved the Blades up to fifth in the Premier League table and to within two points of Chelsea, who occupy the final Champions League spot.
Wilder remains on course to guide the club to their best ever finish in the top flight - currently it is sixth in 1975 - but he is not getting too carried away and is keen to keep his players grounded for the remainder of the season.
Wilder and his team will now fly to Dubai for warm-weather training as they take their winter break.
They will resume their Premier League campaign and their challenge for European football against Brighton at Bramall Lane on February 22.
Asked about the Blades' lofty position in the table, Wilder said: "I'll let everyone else talk about it, I'm just on for the next three points.
"For a promoted side to get to this stage of the season with 39 points is an outstanding achievement, but I don't want us to get comfortable. We are in a fabulous position, we are enjoying it and we want more.
"I'd like it if we had a game next week, but we'll come back refreshed for the next part of the season."
Wilder also had plenty of praise for the character that was shown by his players as they battled back to take another crucial three points.
He was far from impressed with the first 20 minutes and the way Brighton were allowed to dictate the pace of the game and go in front.
However the reaction was very pleasing and Wilder says the belief within the camp is sky high. Wilder also gave a special mention to Sharp.
The Blades skipper, who celebrated his 34th birthday on Wednesday, has not played as much as he would have liked this season and has had to settle for a substitute's role.
He scored his first goal on Sunday since netting against Bournemouth on the opening day of the campaign, and his manager said: "Billy Sharp has not had a lot of game-time. He has had to be patient but he's a fantastic leader in the dressing room."