Campbell struck first on the hour then, after Jake Edwards had pulled one back for the high-flying Brewers, made it 3-1 to book the Shaymen's place in next Thursday's northern final at Rushden & Diamonds.
And it was no less than Halifax, who had taken the lead on the stroke of half time through Mark Whitehouse, deserved after a side showing no fewer than eight changes had given its all.
The attack was a constant threat to the Burton goal while in defence Simon Ainge and Jake Wright were rock solid in front of Craig Mawson.
And Nigel Clough's side, eight of whom had played in Sunday's win over Weymouth when Albion strengthened their grip on fifth place, had no answer.
There was an early scare for Town when Steve Scoffham put the ball in the back of their net after four minutes only to be denied by the offside flag.
But they recovered well and could have gone in front on two occasions in a three minute spell when they opened up the Albion defence.
Thomas Harban's 17th minute crossfield pass picked out Campbell on the left and he cut inside the last defender before firing wide.
And Nicky Gray latched onto a Lewis Killeen flick only to send his shot off target.
Mark Greaves should have given Burton the lead five minutes later but fired over from six yards following a Marc Goodfellow corner on the right.
And Mawson did well soon after to get down and save from Goodfellow after the winger had cut in from the right and fired in a left-foot shot.
It was all Town for the remainder of the opening 45 minutes with Gray firing narrowly wide from the edge of the area and Daryl Taylor, causing problems with this pace on his return to action, hit one over the top from the right when a pass to Whitehouse might have been a better option.
Taylor also headed a Matt Doughty cross narrowly wide before the Shaymen got the breakthrough 30 seconds into first half stoppage time.
Taylor was involved again, finding Campbell on the edge of the area and he fed the ball further towards the left for Whitehouse whose first time shot fired into the roof of the net.
Whitehouse almost had a second soon after the break when he pounced on a defensive error, but his shot on the stretch went across goal and wide.
The Shaymen had to wait until the hour mark before doubling their lead, Gray touching on Harban's throw for Campbell who surged into the area and fired home.
Within a minute, Tom Liversage had crossed for Edwards who headed home from close range.
But any thoughts of a Burton fightback were extinguished when Campbell raced clear in the 63rd minute, steadied himself and lashed a shot past Saul Deeney in the Albion goal.
Town might have had more goals, but there no one was able to get on the end of a Whitehouse cross, Anthony Griffith had a shot from the edge of the area blocked and Tom Kearney was unable to cap a fine run into the area from midfield with a shot powerful enough to beat Deeney.
Burton fought hard in the closing stages and might have pulled a goal back with 11 minutes remaining, but Goodfellow's curling left foot shot from the edge of the area rebounded back off a post and into Mawson's arms.
Ainge did well to repel a Goodfellow corner soon after and the Burton midfielder volleyed wide at the far post from a Shaun Harrad cross.
Good scrambling defence from Wright, Peter Atherton and Harban ensured there was no way through for the visitors.
And Campbell was denied a late chance to complete his hat-trick when he was ruled offside as he looked to get on the end of a Griffith pass.

STAR SHAYMAN
If Andy Campbell needed to remind the Town management what he is capable of, he did it in style last night.
He took his two goals superbly and also had a hand in the opener scored by Mark Whitehouse that put the Shaymen on the road to a superb victory.
While the pacy frontman will steal the headlines, the Town defence also played their part in a stunning evening.
Jake Wright continued his rich vein of form with another assured performance at the heart of the Halifax defence.
And alongside him Simon Ainge, making a rare start since he arrived on loan from Bradford City, also impressed, especially in the second half when Burton threw on Jake Edwards in a bid to get back into the tie.
Campbell takes the three points on offer in our season-long competition with Wright taking two and Ainge one.

PLAYER POINTS
Jon Shaw 43, Simon Heslop 34, Anthony Griffith 22, Tom Kearney 21, Andy Campbell 21, Lewis Killeen 14, Jake Wright 13, Matt Doughty 12, Steve Torpey 12, Steve Bushell 10, Daryl Taylor 8, Danny Forrest 7, Rob Scott 7, Tom Clarke 6, Adam Legzdins 6, Cortez Belle 5, Craig Nelthorpe 4, Craig Mawson 3, Adam Quinn 3, Nathan Joynes 2, Darryn Stamp 2, Ryan Toulson 2, Greg Young 2, Simon Ainge 1, Peter Atherton 1, Gareth Davies 1.

MATCH FACTS
Halifax Town: Mawson, Harban, Dought (Atherton 70), Ainge, Wright, Kearney, Gray, Taylor (Forrest 61), Whitehouse, Killeen (Griffith 46), Campbell. Subs (not used): Heslop, Davies.
Booked: None
Sent-off: None
Goals: Campbell 60, 63, Whitehouse 45.

Burton Albion: Deeney, Hurst (Liversage 61), James (McGrath 70), Austin, Greaves, Holmes, Webster, Goodfellow, Farrell, Scoffham (Edwards 60), Harrad. Subs (not used): Gilroy, Brayford.
Booked: None
Sent-off: None
Goal: Edwards 61

Attendance: 632
Referee: P. Tierney (Wigan)

YOU SAY
Towns amazing cup run continues with stunning goals from mark whitehouse and andy campbell i'm just upset it wasnt fifteen quid to get in - the taxman