Two goals in three second-half minutes courtesy of record signing Pablo Hernandez and Michu were enough to seal a 2-1 win, despite a nervy final 20 minutes after Emmerson Boyce had pulled a goal back for the Latics and Arouna Kone had a header chalked off for offside.
The win was particularly timely given a demanding run of games looming large on the horizon for Laudrup and company.
They head to the Etihad Stadium to face Premier League champions Manchester City next Saturday, before a reunion with former manager Brendan Rodgers when they go to Anfield to face Liverpool in the fourth round of the Capital One Cup.
Chelsea visit the Liberty Stadium the following Saturday and while few will be backing Swansea to pick up a result from that trio of assignments, Laudrup is pleased his players at least head into them with a spring in their step.
He said: "We can work well this week and know we have three games in seven days.
"The good thing is I really don't have to motivate anyone because we have Man City, Liverpool, Chelsea coming up. Everybody is up and that is good.
"We know there is a lot of quality in these sides. We saw what Chelsea did against Tottenham.
"Man City have a lot of quality, they are a great team with (manager Roberto) Mancini. After the last Champions League game they changed seven, eight players and beat Sunderland 4-0. That is a luxury to have when you have a lot of money.
"We know it will be difficult but on the other hand we know they are teams that will let you play. They play well but they lose the ball."
Victory over Wigan comes at the end of a two-week period where the Swans had been stung by reports of dressing room unrest and dissatisfaction among senior players at Laudrup's methods.
The club have repeatedly denied there is any foundations in the reports, while Laudrup has been impressively measured in his own response.
And the Dane remained philosophical despite seeing Swansea record a win that quells such speculation.
"When you win games everything is looked at from a positive angles, and when you are losing there is a negative angle you can find. This time it was this," he said.
"Another day will be another thing, another club. It is never nice when you see something that is like, what is this? Because you know it is not like that, but you have to deal with it.
"We know things come and go and they go much faster when you get a positive result. But we know in all teams there will be unhappy players, because even in the biggest teams if you are not playing you are unhappy. Everybody wants to play. I have talked to the players."
Laudrup sprang a surprise in selection by naming Michu up front as opposed to in his familiar midfield role.
The Spaniard rewarded his manager's faith with a goal, and while Laudrup does not expect to repeat the experiment too often, he admitted Michu's impressive haul of six league goals in eight games makes it an attractive proposition.
"Michu can drop and still be that third midfielder when we don't have the ball," he said. "The thing is he has scored so many goals, he wants to be up there, that is the problem.
"He wants to be up there in the opponent's goal. It is hard for me to say don't. He has scored six plus one in the cup in nine games. That's a good average."
Latics boss Roberto Martinez, meanwhile, is hoping for a change of fortune as his side's own winless run extended to six games.
But he says he will be happy if his side are once again facing a last-day cliff-hanger before securing their Premier League status for another season.
The Spaniard said: "We will take that (a last-day decider), we need to understand who we are. To have eight seasons in the Premier League has been a magnificent achievement.
"The ending of the last campaign is the standard I want for our team the whole season but obviously you are competing with huge budgets and huge clubs and this is the best league in the world.
"So we are prepared to go into the last day of the season but we know we need to start getting points on the board and positive performances, and this was a positive performance."