Swansea 2 Wigan 1
The Dane had been incensed by claims that his squad was drifting apart due to players bringing into question his man management skills and training methods. However, all was forgotten on the final whistle as Hernandez and fellow Spaniard Michu secured a first win in six games for last season's surprise package.
Emerson Boyce halved the deficit, to set up a frantic final 20 minutes during which Arouna Kone had a goal disallowed for offside, but Swansea held on for a welcome victory, in more ways than one.
Laudrup said: "It was a mixture of joy and relief when the final whistle went.
"We did have to suffer a bit in the last 20 minutes but after so many games without winning it was a great result.
"The team is happy always when we win and that is normal.
The difference in football at this level is that there will always be players that play all the games and others who don't. Those who are not always playing will not always be happy." Swansea began as they had two weeks previous against Reading, with no signs of the supposed unrest that has led to far too many prickly questions this week.
Still, just as they wasted opportunities to establish themselves against the Royals, so they did against a Wigan side managed by the former Swansea manager Roberto Martinez.
Michu was guilty of missing the target on three separate occasions while Angel Rangel and Hernandez were careless in their final execution after Leon Britton and Wayne Routledge had carved out successive openings.
Wigan, whose only victory in their opening seven games had come on the road, at Southampton, certainly grew into the game although at times, they struggled to retain possession in a hectic midfield third. However, when they did, Shaun Maloney was denied by a smart save from Michel Vorm.
If the first half had been a little below par in terms of incident, the second started with Swansea inches away from taking the lead.
Hernandez saw his cross cleared by Gary Caldwell but when Britton picked up the loose ball, his shot was inches wide.
Britton's urgency in midfield kept Swansea on the front foot for long periods with Ki Sung-Yeung twice denied by saves from Ali Al Habsi.
Then, with 26 minutes remaining Hernandez, out of nothing, swivelled on the edge of the penalty area and beat Al Habsi at his near post.
Michu's header from a corner two minutes later doubled the lead before Boyce halved it with a spectacular overhead kick 90 seconds after. Thereafter, it was all hands to the pump for Swansea who did at least hold on to a valuable win.
Wigan manager Roberto Martinez said; "I thought we deserved something from the game. However, you need that little bit of sharpness in the final third and we missed that today."
Swansea (4-5-1) Vorm; Rangel, Flores, A Williams, Davies; De Guzman (Graham 83), Routledge, Britton, Ki Sung-Yeung, Hernandez (Dyer 72); Michu Subs not used: Tremmel, Monk, Moore, Shechter, Tiendalli Booked: Rangel 75, Ki 85 Wigan Athletic (3-4-3) Al Habsi, Ramis, Caldwell, Figueroa (Watson 69); Boyce, McCarthy, McArthur (Boselli 83), Beausejour; Maloney, Di Santo (Gomez 83), Kone Subs not used: Pollitt, Jones, McManaman, Miyaichi Booked: Beausejour 73, Maloney 89, Gomez 90
Referee: M Jones (Cheshire)