Roger Espinoza and James McCarthy struck for the home side, but Laudrup's men responded through Angel Rangel and Itay Schechter before Dwight Tiendalli hit the winner 14 minutes from time.
With Wigan battling against relegation, the tension was evident in a nervy first half, with Laudrup admitting Tuesday night's contest was not the best game he had witnessed.
He told Sky Sports: "The reaction and the intensity my players showed in the second half was really great.
"It wasn't a great football game, technically speaking, because there was too much at stake for Wigan.
"I think coming back twice in an away game to Wigan like this, I can be very, very pleased."
Meanwhile, Laudrup confirmed keeper Michel Vorm would fly back to south Wales despite being stretchered off after a nasty clash of heads with Ben Davies.
"Michel seems OK," said Laudrup. "He was a little dizzy and was out for a small time but we will check him again tomorrow."
Although safe, the win ended an awful run of results for Swansea who had not won since beating Newcastle eight matches ago.
"It was important to end that run of bad results," Rangel said. "It was important to get the three points to secure a place in the top 10.
"We know Wigan are fighting relegation, we showed good character."
Rangel's goal could have a big say on if Wigan, a club managed by former boss Martinez, go down.
"I wasn't thinking about that, it was a vital game - hopefully they will stay up," Rangel added.