Ten-man City took all three points at the Pirelli Stadium following Reeco Hackett's low second-half drive.
City started brightly and almost took the lead in the 7th minute when Reeco Hackett’s cross into the box deflected into the path of Lasse Sorensen, but the Dane’s header was superbly tipped away by Max Crocombe.
Albion’s first attempt of the contest came after 25 minutes when Tolaji Bola saw a shot from inside the area take a deflection and drift wide of the far post.
A good block from the host’s defence meant Freddie Draper couldn’t convert Sorensen’s low ball across the edge of the area.
The Imps were reduced to ten men when Alex Mitchell was shown a second yellow card after tangling with Ademola Ola-Ademobi.
Hudlin looked to take advantage immediately but he could only shoot straight into the arms of Jensen.
Burton then caused City danger from a long throw as the ball bounced in the box. Ola-Ademobi managed to get something on the ball but Jensen was able to gather.
The Imps came so close to taking the lead in first-half injury time, but Adam Jackson’s header from close range was held by Crocombe.
After half-time City had another great opportunity to open the scoring, but Ethan Hamilton couldn’t quite keep his effort down after a flick-on found him with space in the box.
Despite their man disadvantage the Imps took the lead in the 54th minute when Hackett squeezed a shot under the body of Crocombe and into the back of the net.
Burton almost responded quickly, with Hudlin gathering the ball on the edge of the box before firing inches wide.
After 64 minutes Ben House replaced Freddie Draper for his first appearance since August and he nearly made an instant impact, but Sorensen teasing delivery just stretched him slightly too far.
City were proving a dangerous proposition on the counter-attack and Hackett nearly grabbed a second with a sweetly-struck drive from just inside the area but this time Crocombe was equal to it.
Hackett continued to cause the Brewers’ defence all sorts of problems with the winger setting Hamilton up for an audacious attempt before whipping in another dangerous cross which Crocombe dealt with.
Albion pushed forward desperately in search of an equaliser but the Imps held strong for a hard-fought victory on the road.
Burton: Max Crocombe, John Brayford (c), Deji Oshilaja (Mason Bennett 60’), Ryan Sweeney, Joe Powell, Jasper Moon (Mustapha Carayol 58’), Kyle Hudlin (Joe Hugill 60’), Mark Helm (Antwoine Hackford 72’), Ademola Ola-Adebomi, Jake Caprice (Bobby Kamwa 46’), Tolaji Bola. Subs (not used): Jamal Blackman, Rekeem Harper.
Imps: Lukas Jensen, Lasse Sorensen, Adam Jackson, Ethan Erhahon, Reeco Hackett (Jack Burroughs 82’), Ted Bishop (Connor McGrandles 82’), Ethan Hamilton, Dylan Duffy (Paudie O’Connor 39’), Sean Roughan, Alex Mitchell, Freddie Draper (Ben House 64’). Subs (not used): Jordan Wright, Joe Taylor, Danny Mandroiu.
Goal(s): Hackett (54’)
Attendance: 3,995
Referee: Jeremy Simpson.