Captain Chris Conn-Clarke spearheaded the Clarets’ march into the last 16 of the FA Youth Cup.
The Northern Ireland youth international earned the early penalty converted by Rhys Fenlon before curling in Burnley’s second goal himself.
And when Dylan Mooney volleyed home a third with less than 20 minutes gone, Tony Philliskirk’s youngsters already had a foot in round five.
West Bromwich Albion now await the Clarets, who have advanced this far only once since their run to the semi-finals of the competition in 2012.
The home tie against the Baggies will be at Curzon Ashton, where Burnley launched their challenge with a 5-0 win over the National League North side.
And they again avoided an upset thanks to a flying start which effectively ended Mansfield’s hopes of prolonging their impressive run in the competition.
The Stags had knocked out Doncaster, Rotherham and Queens Park Rangers to reach round four – all at Field Mill.
But their home advantage wasn’t enough to compete with the Clarets once the visitors had taken early control.
Mansfield couldn’t cope with the pace and trickery of Conn-Clarke in the opening stages and he duly made them pay.
After just 10 minutes his twisting run, following a pass from the impressive Ben Woods, was ended by a trip from Ben Bayliss.
Fenlon, stretching the Stags on other flank, had scored the opening goal at Curzon Ashton from the penalty spot and repeated the dose to calm any early nerves.
Conn-Clarke then took matters into his own hands four minuites later when another positive run ended with the Clarets' top scorer cutting in to bend a shot into the top corner from just inside the penalty area.
Things might have been different had Harry Allen not saved smartly at the feet of Shamar Lawson at the other end with the tie goalless.
Instead, Mansfield were left with a near impossible task when Mooney met a corner from midfield partner Woods inside the six-yard box to add a third goal inside the space of eight minutes to give the Clarets a 3-0 half-time lead for the third game in a row.
The margin could have been even greater if Joe McGlynn had accepted a shooting chance just before the break.
But to their credit, Mansfield – watched by the Stags’ Turf Moor Academy graduates James Clarke and Aidan Stone – responded well and almost pulled a goal back through Lawson, who fired just wide.
And they then had the better second-half chances on a wet and windy night as the Clarets battened down the hatches to see out the tie and secure a fourth successive win in league and cup.
Defender George Cooper saw a combination of Allen and Conn-Clarke keep out his goalbound header before Jimmy Knowles – who has scored at first-team level – shot wide when he looked a certain scorer.
Allen also had to dash off his line to save well at the feet of Joshua Scott.
But while the Clarets enjoyed a three-goal margin they were never under any real threat of letting things slip.
And left-back Matty Rain almost added a fourth – and the goal his performance merited – when he got forward to screw a low shot across the face of goal.
Mansfield: Campbell; Bayliss (King 60), Cooper, Saunders, Sketchley; Molyneux, Hill (Ingram 70), Tomlin, Lawson; Scott, Knowles. Substitutes: Boyle, Fisher, Adams, Jones, Caine.
Burnley: Allen; Patterson, Rooney, Pruti, Rain; Fenlon, Woods, Moonan, Conn-Clarke; George (Thompson 65), McGlynn (Mellon 88). Substitutes: Thomas, Chima, Armstrong, Brennan, Connolly.
Referee: Andrew Humphries