Premier League strugglers Burnley were fast out of the blocks and raced into a 2-0 lead after eight minutes in the third-round replay at White Hart Lane, with the original encounter having ended 1-1 at Turf Moor last week.
Marvin Sordell scored his first Burnley goal since joining in the close-season with a stunning half-volley before Ross Wallace's free-kick went in via a fortuitous deflection off Roberto Soldado.
After an opening 45 minutes that had all the hallmarks of an FA Cup classic, the second half went to script as Vlad Chiriches took advantage of an error from Burnley goalkeeper Tom Heaton to head Spurs in front.
Mauricio Pochettino's side showed their superiority when Danny Rose added a fourth in the 52nd minute and that proved enough to clinch a round-four showdown at home to Leicester City.
Burnley left the home fans stunned by doubling their advantage five minutes later when Wallace's 25-yard free-kick struck Soldado and wrong-footed a helpless Vorm.
Andros Townsend's cross from the right picked out Soldado and his flicked header found Paulinho, who controlled the ball on his chest before swivelling on the spot and calmly volleying home from close range.
The home side were level in first-half injury-time, though, as Ben Davies' cross was only half-cleared and Capoue lashed home the equaliser from the edge of the area.
Heaton flapped at Paulinho's inswinging corner from the right and Chiriches took advantage to nod home at the back post.
Spurs made it 4-2 in the 52nd minute when Benjamin Stambouli's excellent cross-field pass found Soldado and his low centre from the right was met by the on-rushing Rose.
Pochettino's men were well in the ascendancy and Nacer Chadli flashed a cross along the six-yard box, before Soldado dragged wide from distance with just over 20 minutes remaining.
The 17-year-old had little opportunity to make an impact, though, as the hosts comfortably wound down the clock to see off Sean Dyche's men.
