The Swans had won just one of 11 Barclays Premier League home games prior to Wednesday's meeting with the Magpies, but they produced arguably their best display of the season to date to end the visitors' run of four straight wins.
The Welsh club move on to face three games in six days, starting with Monday's visit of Hull, which is followed by the Europa League trip to St Gallen and a league meeting with Norwich.
Victory over the Tigers would move Swansea past halfway on the road to the oft-stated 40-point survival mark, while in Switzerland they can reach the knockout stages of the Europa League.
All that means the timing and manner of the win against Newcastle could not have come at a better time for a side who have not managed to hit their stride so far this term.
"Winning 3-0 and keeping a clean sheet is great and we played a very good side who had a lot of confidence after four wins, that gives us a big boost," said Laudrup.
"All these factors mean this is a huge win and it gives us enormous confidence before facing three games in six days in a very important week.
"If we do well we can go past 20 points and qualify for the knockout stages in Europe for the first time in the history of the club. It is a huge week for us."
The only downside for Laudrup was the loss of a third striker to injury after Alvaro Vazquez picked up a groin problem.
The Spaniard joins compatriot Michu (ankle) and record signing Wilfried Bony (hamstring) on the sidelines.
All three could yet be fit to face Hull on Monday but Laudrup will take a cautious approach.
"Michu has trained on his own, but on Sunday it will be five weeks since he was injured in the Cardiff game.
"Let's say he could be back for Monday but he will definitely not be match fit, so we have to bring him back in carefully.
"He knows he will not be able to play 90 minutes on Monday, Thursday and Sunday.
"It is the same with Bony, the injury is not too bad but it is too soon to say if they will be back for Monday."
After Vazquez's exit, Swansea were forced to play with the diminutive Alejandro Pozuelo as a 'false nine', but they were arguably all the better for it as their passing and movement caused Newcastle all sorts of problems.
Shelvey, in particular, excelled and was named man-of-the-match for a terrific display, which was marred by an incident where he appeared to motion to headbutt Debuchy, although the England Under-21 cap will face no action from the Football Association.
Laudrup was delighted with how his side adapted, but does not necessarily see Swansea operating without a recognised striker regularly.
He said: "We saw the perfect way to play without a number nine as you move ball then have a player like Jonjo coming from deep and that is exactly how you have to play without a striker.
"But, just because you have success one day does not mean it always works, it depends who you play.
"There are different teams you play but it is a possibility and the players have seen with the abilities they have we can play that way, but because we played that way here does not mean we will play that way all the time."