In doing so, they lifted a little of the gloom around the club after a disappointing week, ended somewhat of a hoodoo against Watford this season and set up a two-legged semi-final against Ipswich Town. Southampton play either Derby or Wolves in the other semi-final.
The lads made a stunning start at Vicarage Road with Charlie Daniels opening the scoring in the first minute.
Andy Barcham set up that goal and then scored the second himself with 24 minutes on the clock.
With Tommy Forecast in fine form between the sticks and a collective brick wall of a defence in front of him - Charlie Lee and Leigh Mills outstanding again - there was to be no way back for the spirited home side.
We lined-up with just one change from the fifth round win against Everton with schoolboy Radwan Hamed coming in for the injured Simon Dawkins. Hamed's fellow schoolboys Archibald Troy, Jamie Davis and keeper David Button were all on the bench.
Daniels handed us the dream start with just a minute on the clock. He owed a great deal to Barcham, who crashed through a 50-50 with Adrian Mariappa, reached the byline and crossed low for the winger to side-foot home in style at the near post.
Jamie O'Hara's free-kick caused panic a minute later as keeper Reece Kirk came out but ended punching thin air.
It took 15 minutes for the home side to settle and they forged a chance when Andrew Chapman found space on the left and crossed for Alex Campana whose shot was half-blocked by Phil Ifil and then hacked away by Lee.
It wasn't long before we were back up the other end though as O'Hara's inswinging corner tested Kirk again - the Watford keeper finished second best to high-flying Lee but there wasn't enough power on his header.
Lee's next involvement did lead to a goal though. He spotted Barcham peeling away to the left and hit the perfect pass over the top of both the striker and Mariappa. The chase was on and Barcham out-muscled the Watford skipper for the second time, raced into the left side of the box before measuring his finish across Kirk into the far corner, 24 minutes, 2-0.
Barcham ran the Watford defence ragged in the opening exchanges and another chase to a ball over the top led to the next effort on goal. Once again the striker troubled Mariappa and his poor clearance fell to Stuart Lewis who drilled a first-time shot straight at Kirk from 30 yards.
If Watford were shaky at the back, they were lively up front and we were handed a reminder after 36 minutes. Joel Grant created it with a quick turn and break before feeding Toumani Diagouraga in box, Ifil and Mills got back and launched in to block but Diagouraga got the shot off and rattled the crossbar.
Always competitive, Watford won a free-kick on the stroke of half-time but Junior Osborne smashed it into the stand.
As expected, Watford came flying out in the second half and caused an early problem for Forecast when Jordan Parkes' attempted cross was heading for the top corner until the keeper's timely flick over.
With Daniels off the pitch injured and us down to 10 men, Forecast was forced into his first action of the night in Watford's best spell so far, a low save down to his right from Al Bangura's shot after 56 minutes. The same player then had an effort deflected just wide. Jamie Davis eventually replaced the limping Daniels.
Davis was soon into the action, his cross from the right drifting over Kirk but too deep for Barcham to head back into the danger area.
Forecast, looking confident and solid, then produced the save of the night, a flying tip over the bar from Ryan Gilligan's 25-yard dipper on the hour mark.
Watford were pressing now and struck the woodwork again after 64 minutes. Lee was cautioned for a trip on Grant on the edge of the box and Diagouraga's curler beat Forecast only to hit the top of the crossbar and bounce to safety. Forecast then had to make a more routine save to his left to keep out Gilligan.
Play switched to the other end and a great chance, Mariappa's back header intended for Kirk was short, Hamed nipped in but Kirk stood up well to save the one-on-one.
After a relatively quiet spell, the next goalmouth action after after 75 minutes as the lively Grant broke into the box but ran into a brick wall in Lee and Mills - the pair there again to block when Chapman sniffed a half-chance in front of goal with five minutes left.
Gaps were opening up as Watford pushed forward and we almost exploited it when Davis found himself in the box only for Kirk to push away his effort, the rebound fell to Hamed who dragged it into the side-netting.
1min: GOAL. Barcham won key 50-50 with Mariappa, continued run down left channel, cut back to near post where Daniels finished well.
Watford 0, Spurs 1
15mins: CLOSE. O'Hara floated in corner, Lee beat Kirk in the air but couldn't quite get enough on his header which was cleared.
24mins: GOAL. Barcham again won 50-50 battle with Mariappa to reach Lee's perfectly-weighted pass, took ball into box, left channel, slid home superbly from tight angle.
Watford 0, Spurs 2
36mins: WOODWORK. Quick turn and break from Grant, he laid ball into Diagouraga in box, Ifil and Mills launched in to block but Diagouraga got shot off and rattled the crossbar.
56mins: SAVE. Forecast down low to his right to tip Bangura's shot around the post.
60mins: SAVE. Forecast flying tip over from Gilligan's dipping 25-yarder.
64mins: WOODWORK. Diagouraga's curling free-kick beat Forecast only to hit the top of the crossbar and bounce to safety.
68mins: SAVE. Mariappa's header back to Kirk was short, Hamed nipped in but Kirk saved one-on-one chance to his left.
89mins: SAVE. Kirk reaction save to deny Davis and then Hamed dragged rebound into side-netting.
Watford: Kirk, Osborne, Parkes (Frost, 70), Mariappa, Homand, Diagouraga, Campana (Matthews, 76), Bangura, Grant, Chapman, Gilligan. Subs: Bardle, Hoad, Cader.
Spurs: Forecast, Ifil, Mills, Lee, Wright, Maghoma, Lewis, O'Hara, Daniels (Davis, 56), Hamed, Barcham. Subs: Riley, Button, Troy, Seanla.
Our Under-18s progressed to the semi-finals of the FA Youth Cup with a superb 2-0 win at Watford on Thursday night.