Watson suffered a double fracture to his right leg in the Latics' previous 2-0 victory over Barnsley, and Rosler felt his players delivered the perfect response to the injury blow.
Goals in each half from James McArthur and Chris McCann gave Wigan their fifth win in six games in all competitions before a crowd of 27,470 at the Amex Stadium.
Brighton, wasteful in front of goal, reduced the deficit through striker Leonardo Ulloa 12 minutes from time, but could not force and equaliser as they went down to their first home defeat since December 3.
"This was a big win for us and it is dedicated to Ben Watson," Rosler said.
"He had his operation yesterday and the reaction of the players to his injury was first class. They showed will power to get that win and not to get beaten."
Rosler confessed that his men had to withstand considerable pressure in order to come out on top, adding: "We were on the back foot for the first 20 minutes and our goal came against the run of play.
"Brighton are a good footballing side. We have players missing and the loan players we've brought in had to adjust to our style of play.
"We made up for it with an enormous amount of effort. For the first 20 minutes of the second half Brighton struggled and we scored again.
"For the last 15 minutes it was backs to the wall and fortunately lady luck was on our side."
Wigan have now lost only two of their past 17 games in league and cup, but Rosler is refusing to get carried away regarding their play-off prospects.
He said: "We will keep our feet on the ground for sure. We have to improve as a team and individually."
Brighton head coach Oscar Garcia blamed weakness in front of goal for his team's first defeat at home in nine games.
"We had 20 chances yet we only scored one goal. Wigan had two chances and scored two goals," he said.
"We should have scored more than two for sure; we fully deserved to win. We dominated the whole game.
"I can take positives from the performance, but what is less positive is that we need to be more clinical in front of goal.
"Wigan came here to sit back, the only thing they did better was to score; we expected a more offensive Wigan.
"They respected us. We dominated the whole game, had the better chances but we weren't clinical enough in front of goal."
Argentinian striker Ulloa now boasts four goals in the past four games but Garcia said an ankle injury means that his star man is not fully fit.
"Leo is trying his best and I will see how the players are ahead of our FA Cup replay at Hull on Monday," he said.
"Some of them are really tired and we have some knocks, but I can't complain. We are flying there and will do our best. We will have a go."