Then they made a mistake and conceded.
When Sheffield Wednesday concede first, they invariably lose. This time it was 2-0.
The gap to safety is still seven points, but the Owls now only have 15 to play for. Coventry City have 18.
Moore likes to play modern football, asking his players to pass in tight quarters, even in their own half. Julian Borner bombed forward enthusiastically from left-sided centre-back, Josh Windass and Jordan Rhodes worked hard and made good runs.
But it involves risks at times, and yet to have a transfer window in charge or much time even on the training ground, Moore does not yet have quite enough of the players to play his way.
Borner showed how it should work at the end of the first half, beating Andre Ayew deep in his own half and clipping a ball which deserved a better touch than it got from Liam Shaw.
The problem is, it did not always work.
Tom Lees at his best is a proper defender, but not a ball-playing one. When he let a pass run across him in the 32nd minute, Ayew robbed it, nudged the ball across for Jamal Lowe and the Owls went behind. The confidence they had been building left them.
Looking at the game as a whole, it had not been coming, but Lees served warning when caught overplaying in the ninth minute. Wayne Routledge, often a winger in his career but central in Swansea's front three, cut the ball out and his side won a corner the Owls defended.
When Liam Palmer have the ball away Sam Hutchinson, dropped into a back three, did well to dispossess Lowe.
Had that been the extent of the damage, it would have been worth it.
Joey Pelupessy had a shot blocked in the 13th minute when Borner was on his toes to get in front of Ayew as Joe Bennett tried to pick him out. Soon the German was forcing his way down the inside-left channel, only for Marc Guehi to cut out his ball in.
Windass and Rhodes did well to pressure Routledge into conceding a corner but a backpedalling Rhodes could not get his header under the bar from it.
When Bannan won the ball in midfield, Wednesday found Shaw, in the hole of a 3-4-1-2, via Adam Reach and Freddie Woodman made an excellent left-handed save. So to be behind five minutes later was a killer blow, particularly giving the Owls' record when conceding first. It is December 2019 since they last won that way.
Although Windass lobbed onto the roof of the net a minute later, the goal affected both sides. Ayew beat Borner at the byline but could not get the ball through the crowd scene in the Owls box. Ryan Manning shot well over when a corner was pulled back to him.
The mistakes kept coming after the interval, though Hutchinson and Rhodes, with a very good slide tackle, at least made up for giving the ball away but quickly winning it back.
Swansea noisily appealed for a penalty when Borner tackled Kyle Naughton in the penalty area.
They kept making chances too, Windass found by an excellent pass from midfield and cutting across the area on his left foot before Ryan Bennett blocked the shot.
In the 70th minute he did brilliantly to take Liam Palmer's chipped cross off the head of substitute Callum Paterson. A minute later the wing-back was in again and took the low road, only for the ball to be booted clear.
But the threat was not all one way.
“Head it! Head it! Head it!” the recalled Keiren Westwood screamed as Borner dithered over a bouncing ball. When he finally did, the weak touch let Ayew in, and Westwood had to come off his line to sort things out himself.
In the 74th minute, the freshly-introduced Connor Roberts showed Palmer how it was done, peeling from centre-forward out to the same flank and putting in a left-wing cross Jay Fulton headed in.
Victory moved Swansea up to third, four points ahead of Barnsley.
Sheffield Wednesday: Westwood; Hutchinson, Lees, Borner (Green 76); Palmer, Pelupessy, Bannan, Reach; Shaw (Brown 65); Windass, Rhodes (Paterson 65).
Unused substitutes: Wildsmith, Urhoghide, Penney, Hunt, Harris, Kachunga.
Swansea City: Woodman; Naughton, Bennett, Guehi, Manning (Bidwell 75); Fulton, Grimes, Hourihane (Smith 80); Ayew, Routledge (Roberts 73), Lowe.
Unused substitutes: Whittaker, Hamer, Dhanda, Latibeaudiere, Cooper, Freeman.
Referee: M Donohue (Greater Manchester)
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