Steve McClaren's team had won their previous four games at the iPro Stadium but only really threatened after Beausejour had fired the visitors into a 68th-minute lead.
Simon Dawkins and Chris Martin had chances to level but Wigan held out through five minutes of stoppage time for a victory which was sweet for Rosler, whose Brentford team had been thrashed 5-0 at Derby in the Capital One Cup in August.
Derby had beaten Wigan 3-1 at the DW Stadium a month ago but the visitors have improved under Rosler and they had a chance to take the lead in the 17th minute.
The ball was fizzing around on the rain-soaked surface and a quick Derby break down the left ended with Jamie Ward delivering a low cross that was just too close to Latics goalkeeper Ali Al Habsi.
Johnny Russell found Craig Forsyth in space in a similar position in the 25th minute but the Derby left-back sent his cross sailing harmlessly over the bar and Wigan skipper Emmerson Boyce was also off-target with a header from a free-kick four minutes later.
Powell jinked past two defenders before going down in the box in the 33rd minute but referee David Webb booked him for diving and another promising Wigan move ended with a James McArthur shot that just dipped over the crossbar in the 37th minute.
Wigan were getting in good positions without making them count and Rosler showed his frustration when Beausejour put a cross into the side-netting and Espinoza put a volley wide when Marc-Antoine Fortune headed down a cross in the 45th minute.
But the visitors finally broke through midway through the second period with substitute Callum McManaman playing a part after Powell had won a corner.
When it was taken short, McManaman exchanged passes with Beausejour who lashed a left-foot shot from the edge of the box over Rams goalkeeper Lee Grant.
Derby had created little but they should have equalised in the 74th minute when Conor Sammon escaped down the right and set up Dawkins but he took a touch and his shot was deflected wide.
Wigan survived another scare three minutes later when Al Habsi could not hold a skimming drive from Will Hughes but recovered to save the rebound from Sammon.
Derby were enjoying their best period of the game and they had another great chance in the 85th minute when full-back Andre Wisdom crossed to the far post but top scorer Martin put the ball wide.
- Sports & Recreation
- Chris Martin
- Nick Powell
- Roger Espinoza
- Simon Dawkins