The Owls had not played at S6 in League One since drawing with Wycombe Wanderers on November 27 last year.
The emphatic result was even more impressive, considering it was the Owls’ first win over Plymouth in four attempts this season.
Following back-to-back away defeats at Sunderland and Shrewsbury Town, Wednesday dominated the opening 45 minutes and should have had more to show than goals from Sylla Sow and Nathaniel Mendez-Laing.
Plymouth cut the deficit at the start of the second half with a stunning free-kick from Adam Randell.
Sam Hutchinson restored Wednesday’s two-goal cushion, before two goals in a minute.
A goalmouth scramble saw Marvin Johnson credited with an own-goal, before Wednesday went up the other end and substitute Josh Windass secured victory with a clinical strike.
“We haven’t had a game here for seven weeks so it was really pleasing to put on a performance like that today in front of our own supporters,” said Moore.
“The plan was to go for them and the players did that, Plymouth couldn’t really settle but we made it really difficult for them.
“I don’t think anyone would deny us those three points today.
“We dominated the game and although Plymouth scored two goals, I never felt like we were not going to win that match.
“We had too much for them today, we came for the three points and we have the three points.”
The Owls made a bright start, Lee Gregory causing trouble for the Plymouth defence, before Jack Hunt fired into the side netting.
They came close to breaking the deadlock when Hunt’s cross was headed towards goal by Gregry, but was thwarted by goalkeeper Michael Cooper.
But from the resulting corner, Hunt again crossed and Sow sidefooted home.
Wednesday were dominating the game and after a fine run by Massimo Luongo, the midfielder picked out Gregory, but the striker smashed shot against the post.
Barry Bannan had the next chance to make it 2-0, bursting clear with just the keeper to beat, but shot wide from 18 yards out.
But on 38 minutes, the Owls did double their lead. Mendez-Laing beat the offside trap, burst down the left flank, cut inside before curling low beyond Cooper.
Moments later Mendez-Laing nearly added a third, but his near-post shot was blocked by a defender, with Gregory frustrated a pass didn’t come his way.
Fisayo Dele-Bashiru blazed over after a break from Sow, and a third goal would not have embarrassed the Owls for a dominant opening 45 minutes.
But it was the visitors who scored next. Plymouth pulled a goal back within a minute of the restart, Randell firing in a free-kick from 25 yards.
Luongo saw his goal-bound effort blocked, Bannan dragged an effort wide, before going much closer with a curling shot which just fizzed wide.
Bailey Peacock-Farrell came to Wednesday’s rescue, plucking a header from Conor Grant out of the air.
And that intervention proved crucial as centre-back Hutchinson made it 31, heading home Hunt’s cross from close range.
It looked set to be a nervous last seven minutes when Johnson diverted the ball into his own net.
But Wednesday killed the game off within seconds of the restart, Windass drilling home in front of the Kop.