When referee John Brooks blew the final whistle after five minutes of stoppage time, the monumental relief that a win brought was clear to see among Pulis and his players.
That was understandable given their recent run as Tom Lees’s 67th-minute header stopped the rot and lifted the Owls off the foot of the table.
The win ended an eight-game winless run since Pulis replaced the sacked Garry Monk at Hillsborough.
It meant Wednesday can enjoy Christmas without being completely haunted by the nightmare of relegation to League One, although in reality, a grim fight lies ahead.
A mightily-relieved Pulis said: “Winning is everything and hides a multitude of sins. I’m delighted for the dressing room and the supporters who have waited a long time for that.
“We need to make this a fortress and that hasn’t been the case of late.”
Indeed, the result marked just Wednesday’s second home win of the season, Pulis having made three changes from the team that lost to Nottingham Forest on Tuesday night. Keiren Westwood replaced Joe Wildsmith in goal, Liam Palmer came in for Moses Odubajo and Callum Paterson took the place of Joost Van Aken, who dropped to the bench.
That victory was achieved by Owls stalwart Lees on his 250th appearance for the club was apt.
When captain Barry Bannan delivered a left-wing free-kick, Lees nodded home at the far post for his first goal in almost a year.
Putting your head in where it hurts has to be Wednesday’s mantra if Pulis is to keep them up.
Josh Windass missed chances and should have made the game safe late on but fired straight at Coventry goalkeeper Ben Wilson.
Windass admitted: “It wasn’t my day in front of goal. I’ve been moaning I haven’t been getting any chances and then here I did but didn’t put any away.
“Even by half-time I’d missed a couple and I’d been thinking ‘get the next one’.
“The one at the end, I had loads of time and thought about passing it to Jordan (Rhodes) but then changed my mind.
“I don’t know what was going through my mind, but the lads dug me out and we got the win, so that was all that mattered.”
At the other end, recalled Wednesday goalkeeper Westwood made a number of saves to keep Coventry – previously unbeaten in eight – at bay.
Windass added: “It’s not been good enough the past nine games – we should not be where we are. But if I can put the chances away and the lads can do likewise then we can start scoring goals and getting up the league.
“When you play for a big club you are expected to win and that’s the be-all and end-all.
“Criticism that comes your way, you deserve, but hopefully we can turn it around. This was a massive win.”
Wednesday’s recent form has not been helped by an ongoing issue with the non-payment of player wages.
Windass said diplomatically: “It’s like anything, if you lose, people will say it’s affecting you and if you win, it’s not. I’m just here to play football and score goals.”
Bannan was forced off with a late hip injury and will be assessed ahead of the Boxing Day trip to Blackburn Rovers.
Pulis, who has never been relegated during a 28-year managerial career, added: “It’s a long old season and there are enough games left to put a run together to stay in the division.
“They’re a good group of lads but we need to improve and we need reinforcements in January.”
Coventry manager Mark Robins was proud of his side despite seeing their eight-match unbeaten run end.
The former Rotherham, Barnsley and Huddersfield chief said: “It’s been a really difficult day. We are disappointed, but certainly not with what we’ve done over the past nine games.
“We didn’t do enough this afternoon and we weren’t ruthless enough in front of goal. We created decent opportunities and we had the ball in decent areas, but we didn’t make the most of it.
“I’m not going to make any excuses, but the pitch was horrific. The pitch meant that we couldn’t get any momentum.
“Sheffield Wednesday were fighting and hadn’t won since Tony came in. It’s a disappointment for us because we couldn’t keep our run going.
“We showed a lot of intent to try and score a goal, but that was difficult because of the pitch.
“No heads should be hanging. The lads did fantastically well and gave me everything that they had.
“Energy-wise, I thought we were not too bad either. We have to move on from this really quickly.”
Sheffield Wednesday: Westwood, Palmer, Lees, Dunkley, Reach, Harris, Paterson, Pelupessy, Bannan (van Aken 83), Shaw (Rhodes 64) Windass (Kachunga 90). Unused substitutes: Wildsmith, Dele-Bashiru, Penney, Urhoghide, Brown, Hunt.
Coventry City: Wilson, Ostigard (Giles 73), McFadzean, Hyam, Dabo (Dacosta 72), Sheaf (Kastaneer 83), Allen, McCallum, O’Hare, Walker (Bakayoko 42), Biamou (Godden 73). Unused substitutes: Camp, Pask, Shipley, Bapaga.
Referee: J Brooks.
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