A brace from striker John Marquis, along with a first senior goal from Brooke Norton-Cuffy was enough to get all three points despite Saido Berahino's 32nd minute equaliser for Wednesday.
After the game, Appleton addressed the media, answering questions about his opponents on the day, Lincoln's performance, The Imps’ home record, his strikers and Norton-Cuffy.
On matching Wednesday and Lincoln's performance
"They've got Championship experience but we matched them, we went toe to toe, I'm really pleased with the aggression we showed today all over the park.
"I thought we were excellent out of possession, we had that little bit of quality when we needed it.”
Appleton praised his side's performance in the second half, saying that that his players were able to press and attack the game even when in front.
He also said that his players were calm when under pressure.
Lincoln were able to play with great intensity and desire during the game, often taking the game to Wednesday and they had a lot of joy when doing that.
The Imps were able to take an early lead through Marquis, weather the Wednesday storm for most of the first half and then dominate the second half to grab a deserved victory against the play-off hopefuls.
It was a performance that Lincoln fans will want to see repeated in coming games, having been on a poor run of form before the game which had led to pressure being on Appleton ahead of the tie.
The only real concern from the game will be the injury sustained to goalkeeper Josh Griffiths in added time in the second half which saw him forced off.
Appleton said he did not yet know the extent of the injury but it would be important that the club knew as soon as possible.
On The Imps' home record
"You look at some of the games that we have got coming up like Sunderland, I'm hoping and guessing that'll be something similar in terms of atmosphere.
"We needed a hostile atmosphere type of game to try and hit back."
Lincoln's run of form at home had been dismal until their victory against The Owls, having won only one of their last six games at the LNER Stadium.
Appleton suggested that the hostility created by the Sheffield Wednesday fans at the game created the tension that The Imps needed to succeed on the day, perhaps giving his side motivation.
The victory is a massive one in the context of their season, as the shock win lifted Lincoln seven points above the drop zone, and they have at least one game in hand on each side in the bottom four.
Appleton pointed to the upcoming home fixture against Sunderland on March 19 as the next opportunity for The Imps to showcase their best football in front of a home crowd.
The fact that the players have proven their ability to beat a side of the size and stature of Wednesday will surely be a boost for them as they approach a difficult string of games.
That said, a home run of form may not be at the forefront of Appleton's mind at the moment, as Lincoln will be the visitors for six of their next seven fixtures.
On Lincoln's strikers
"I thought the front two set the tone and that was backed up by those behind them.
"[John Marquis] will be pleased with the second goal he got because it was a really controlled finish."
Appleton's decision to go with a front two came as part of a tactical switch, and it paid dividends as Tom Hopper and Marquis combined successfully to cause Wednesday all sorts of trouble.
Marquis' performance in front of goal was impressive, scoring a poacher's goal at the back post early on and drilling a shot past Bailey Peaock-Farrell to get his brace on the day.
The Imps' boss was also pleased with the creative side of Marquis' game, getting an assist for Norton-Cuffy's goal which Appleton said he got the weight of the pass just right for.
Hopper was effective as a support striker for Marquis too, and was unlucky not to score when he looped the ball over Peacock-Farrell, only to see Sam Hutchinson on the line, who headed the ball over the bar.
Lewis Fiorini also had a good game behind the strikers, occupying spaces in the midfield and driving at the heart of the Wednesday defence, creating the hosts plenty of opportunities.
On Lincoln's formation
"From an availability point of view we're lacking numbers on the left hand side which might force our hand [on whether Lincoln can use the 3-5-2 again].
"I was quite happy with the formation, we've had two and a half training sessions working on it and picking the right time to use it, but I thought the lads looked okay in and out of possession."
The tactical switch was mentioned by both managers in their post-match press conferences, as Wednesday boss Darren Moore gave credit to the hosts on the day for how quickly they were able to adapt to the new system.
It appeared that Lincoln had lined up with a 3-5-2, which matched the formation their opponents went with to try and compete with The Owls.
This was a clear success for Appleton, and a formation he may want to consider using again in the future, as Appleton had tried a 4-2-3-1 and 4-4-2 system in recent weeks with no success.
The new formation, along with errors from The Owls, created pockets of space for The Imps, who took full advantage of the extra time and space they were afforded, especially going forwards where they were clinical.
"I've been saying it behind the scenes, I think he will play for Arsenal's first team on a regular basis, it might not happen for a couple of years but it's definitely going to happen.
"He had made his mind up before he even hit it what he was going to do with it and I'm delighted for him."
Speaking after the right back scored his first goal in senior football, Appleton was full of praise for the teenager.
Norton-Cuffy was able to effectively complete both sides of the game on Saturday afternoon, defending well when called upon and proving a great creative influence as well.
The Arsenal loanee was a thorn in Wednesday's side throughout the game, and arguably would have been the best player on the pitch had Marquis not scored a brace and assisted Norton-Cuffy on the day.
Appleton clearly has high hopes for Norton-Cuffy in the future, and it seems that his boss feels he can cope with the expectation currently being placed on him.
Appleton also said that he had faith that he would be able to help develop the weaknesses in Norton-Cuffy's game.
Norton-Cuffy would have left the LNER Stadium knowing he had done all he could to impress his parent club after an impressive performance against The Owls.