Alfie May opened the scoring with a deflected shot after four minutes, but Massimo Luongo levelled for the Owls three minutes later.
Wednesday continued to press for the advantage, and it came on the hour as Lee Gregory netted his first goal in eight games with a sublime strike from 25 yards.
Jack Hunt and George Byers scored late on to confirm a vital three points that saw Wednesday leapfrog Sunderland into sixth.
“Mentally and physically, for us, it is a good position for us to be in, but we still need to just continue working,” said Moore.
“We will continue to just focus on us on what we’re about and what we’re doing, and we know that there is another round of games in the week, and it is what it is but we can only focus on and move onto next Saturday, which we have another home game and we will focus on it.
“It was a tough game for us today and a rewarding one, so to be in those places now is great for us.
“It was a good, open, end-to-end game today and credit to Michael [Duff] and his team because I thought they were excellent today and you can see why they have made wonderful progression this season in the league and why they are where they are.
“They sat in a mid-block, waited, broke out when the opportunity came, and put their foot on it with strong, powerful passes and when we did come out, they tried to play it in and behind us.
“When the first goal went in, I was pleased with the reaction to get back into the game.
“We made one or two little adjustments at halftime, and we just felt that if we could keep going then the chances would be there for us with the way we were attacking them, and once Lee Gregory scored that great goal it settled us down.
"At 2-1, there were a few incidents where Bailey [Peacock-Farrell] has made a few saves, there was a block tackle [from Harlee Dean], and they have hit the upright. But Jack Hunt has scored a wonderful goal and it took the game away from them.
“The big thing for me was being here at home and really being in front of our fans and continuing the good form – that’s five home games and 18 goals scored – and I was pleased we could continue that today.
Lee Gregory gets his goal
Forward Gregory netted for the first time in 105 days, which was a strike in a 2-0 win over Crewe Alexandra in December.
However, the 33-year-old has only made nine appearances due to an injury suffered in January.
Gregory makes Wednesday tick with his off-the-ball movement and by doing the ugly side of the game. But his goal against Cheltenham was a moment of quality, something Moore expressed after the day, saying: “It was a great goal.
“He has had his injuries and since he has come back, we have had to get some minutes into him: 60 minutes [against Cambridge United] then 30 minutes against Accrington [Stanley] and then another 60-odd minutes against Gillingham before having the week to work with him. We feel like he is in a position to complete games now.
“He last scored against Crewe and what an emphatic goal it was. He picked it up and you could see he was in total control of it, and he took the finish really well and hit it into the bottom corner.
“To get our ‘number nine’ scoring again was really important at this stage of the season.”
On Harlee Dean’s return
Dean made just his third start since joining the club after a calf injury sustained in their 2-0 victory over Morecambe.
The 30-year-old played in the central position of a back three, with Jordan Storey and Sam Hutchinson on either side of him.
Moore explained that it was good to have Dean complete a full game, as well as his selection headache with the likes of Chey Dunkley and Dominic Iorfa returning from injury.
He added: “What we did today was that Harlee came back in and the good thing is if we had a midweek game, you would struggle to see Harlee play but we don’t, so he has had 90 minutes. Dominic Iorfa had the two games and then we rested him.
“We feel like they are more or less in a position to all complete 90 minutes and play and have that repetition of games.
“We will assess them over this week and as I said, they are in a position where they are building up their strength and we get another week with them because all of them have been out with an injury at some point.
“I want to have them all fit and all strong and have them in a position where if they are doing it then they will stay there and continue – we feel like we are nearly at that point.
“The central player is crucial because their reading of the game has to be spot on. Harlee was spot on and Hutch off the left did well alongside him and Jordan did really well but had just run out of steam, so we didn’t take any risks with him, and we quickly changed him with Dominic Iorfa to solidify that right-hand side.
“We will assess them over this week and select the defenders who we feel are right for next week’s game to get the job done.”
Milestones for two Owls
Sam Hutchinson and Barry Bannan made their 200th and 300th respective appearance for Sheffield Wednesday against the Robins.
Hutchinson signed for the club in 2014 initially on loan from Chelsea before joining permanently that summer, becoming a cult hero with his bullish performances. He was released at the end of his contract in 2020 but returned six months later after a short stint in Cyprus.
Bannan arrived on a free transfer from Crystal Palace and instantly became a hit with the club, helping Wednesday to back-to-back play-off finishes in the 2015/16 and 2016/17 seasons. The Scotsman is a fans favourite and is currently the club captain.
“What the supporters need to know is that those kind of things are going out of the game now with players spending 200-300 games at one club and we have two that have done it today with Hutch making his 200th appearance and Baz making his 300th, so it is wonderful for those,” continued Moore.
“I thought Sam was solid, reliable, and read the game well, so I am really pleased that on his 200th appearance, we got the three points today.”