Eddie Howe made a winning home start as Burnley manager as the Clarets did just enough to make it into the fifth round of the FA Cup.
The Clarets advanced to the last 16 for the second time in six years but were pushed all the way by Burton.
Chris Eagles proved the difference with two goals to his take his season's tally into double figures before Martin Paterson made a welcome return with a late third to finally kill off the League Two side.
Chris Eagles puts the Clarets ahead
Eagles, again playing in a central role, was denied the first hat-trick of his career by inches as he hit the bar in the second half but his goals either side of the break gave Burnley the breathing space to survive Burton's late fightback.
Calvin Zola's 80th-minute goal made it a nervy finish but with Paterson ending his long injury absence with an injury-time strike, Howe's men snuffed out the prospect of an upset and stretched their unbeaten run to five games.
Howe had shown his hand by naming the same side that won at Portsmouth in mid-week and the Clarets started as though they wanted to put the tie to bed early on.
Eagles hit a free-kick against the Burton wall and fizzed another just wide, while goalkeeper Adam Legzdins almost spilled a free-kick from Danny Fox into his own net.
But having survived their first test and doubtless shaken off a bit of rust accrued through their lack of action since beating Middlesbrough in round three, the Brewers showed the spirit that has given them their best ever run in the competition.
The underdogs were undaunted in trying to take the game back to Burnley with new signing Calvin Zola a willing target up front and Jacques Maghoma and Scott Malone offering a threat down the left flank.
And then makes it 2-0
And when a run by Malone was ended by a foul from Clarke Carlisle with 20 minutes gone, the left-back picked himself up and curled the free-kick against the bar as Carlisle went into the book.
The Clarets needed a goal to gain control of the tie and after half an hour it came through the dancing boots of Eagles.
After Jack Cork had opened up the way with an impressive run of his own, Eagles took on the baton and weaved his way magnificently past three yellow shirts and into the penalty area where he kept his cool to slide his ninth goal of the season into the bottom corner of the net.
That was the not the key, however, for a stroll into the last 32 as Burton battled away and prevented the Clarets from clicking into cruise control.
Jay Rodriguez let a chance slip away when he dallied in the penalty area and when Steven Thompson saw his shot saved by Legzdins after Rodriguez and Dean Marney had broken at pace, Howe's men had just a 1-0 lead to take into the break.
The fragility of that was demonstrated almost straight away as a minute into the second half Aaron Webster almost sniffed out a cross from Andy Corbett at the near post.
Martin Paterson returns in style
And with the Clarets rarely threatening a second goal, bar a Carlisle header from Fox's cross which flew wide, Howe waited for little more than hour to make a double change with Chris Iwelumo and Ross Wallace asked to provide more of a cutting edge.
Surprisingly Wallace took a berth wide on the right but that allowed him to cut in onto his favoured left foot and eight minutes after coming on he let fly with a rasping drive which was far-corner bound until Legzdins sprung to his right to make a fine save.
Sadly, though, for the Brewers' keeper that was as good as it got as he was involved in the 70th-minute mix-up which allowed Eagles to seemingly kill the tie with his second goal of the game.
Legzdins' goal-kick comically bounced off defender Darren Moore and when Cork released Wallace, the Clarets had three men bearing down on goal.
Wallace's cross reached Iwelumo beyond the far post and although the big striker could not direct his effort on goal, Eagles was on hand to finish the job from close range.
Eagles had been the Clarets' shining light in attack and with 15 minutes to go he almost completed his hat-trick when he darted past Corbett and sent a fierce angled drive against the underside of the bar and out off the goalline.
Paterson then steered an effort into the side netting as he made a welcome return from the bench after two-and-a-half months out with a thigh injury and teed up Wallace for a chance which he skied over the bar.
And those close calls suddenly gained in significance when Burton pulled one back to make it 2-1 with ten minutes to go.
Malone had been a decent outlet for the Brewers all afternoon and when he got a cross in the right place, Zola pounced to steer home a shot which this time bounced over the line via the underside of the bar.
Suddenly Burton sensed a chance of glory and the minnows had the chance of levelling with seven minutes to go when Adam Bolder slipped in substitute Greg Pearson and Lee Grant had to be alert to save his angled shot.
Turf Moor breathed a collective sigh of relief before Paterson removed all doubt in added time when he showed his poaching skills had not been dulled by following up a Wallace free-kick to side-foot home the third goal and secure a place in Sunday's draw.
Good to be back!
Burnley: Grant, Mears, Carlisle, Duff, Fox, Marney, Cork, Rodriguez (Wallace 61), Eagles, Thompson (Iwelumo 61), Elliott (Paterson 73). Subs: Edgar, Alexander, Bikey, Jensen.
Booked: Carlisle 20, Marney 41
Burton: Legzdins, Corbett (Austin 88), Webster (Young 64), Stanton, Moore, Maghoma, McGrath (Pearson 64), Bolder, Zola, Malone, Penn. Subs: James, Phillips, Boertien, Poole.
Booked: Moore 90
Referee: John Moss.
Well played: Lee Grant and ex team-mate Paul Peschisolido