In a tight encounter of few chances, Barnard broke the deadlock on 62 minutes and Sutton swiftly put a gloss on the scoreline three minutes later.
It was just reward for the boys, playing in their first home game of the competition, who put on a gritty and determined display of no little endevour in the swirling rain at White Hart Lane. They defended stoutly against a strong Blackburn team and restricted them to little in the way of shots on goal.
Usual skipper Ben Bowditch was considered fit enough for a place on the bench after missing the last round and recent games due to a foot injury.
The only change from the team that triumphed at Leeds in round five came at left-back, where Marcel McKie replaced Chris Herron. Paul O'Donoghue lined up alongside skipper Ronnie Henry in central defence and Stephen Kelly operated at right-back.
Mark Hughes and Dean Marney occupied central midfield with Lee Barnard and Nicky Wettner playing right and left respectively. John Sutton and Jamie Slabber spearheaded the attack.
A great crowd turned up at the Lane to support the boys, creating an enthusiastic and sizzling atmosphere that the teams appeared to feed off. This might explain the, for the most part, frenetic opening to the game.
There was some lively sparring going on as the teams measured each other up for potential threats, but it was a first period of containing clear shots on goal.
The first threat to emerge from the game was Kelly down the right. His first cross of the game was intercepted before Sutton could plant a header in on goal.
Kelly was certainly in the thick of the game during the early stages, getting forward and tracking back with ease due to his great speed of foot.
There were some sturdy challenges going in and Marney was somewhat unfortunately shown the yellow card by referee Mr Habgood after 24 minutes following a collision with Ciaran Donnelly. From the resulting free-kick Jerome Watt's free-kick flashed over.
Minutes later, the same player rattled keeper Rob Burch's side-netting from an angle as, towards the 30 minute mark, Blackburn were beginning to establish some territory.
Jermal Johnson burst through to the right of our penalty area and unleashed his shot only for it to be met full on by the advancing Burch, who made a brave stop. The loose ball was blasted over the bar.
Spurs clawed their way back with grit and determination. Marney's free-kick from 40 yards out was just missed at the far post by a Sutton lunge, while the boys nearly took the lead on the stroke of half-time.
Barnard beat his man down the right and clipped a pass in that was just missed by Slabber on the turn.
The second half began in much the same vein as the first ended. Both teams appeared to be adopting a 'thou shalt not pass' attitude and were very disciplined in defence with the prize at stake a coveted two-legged semi-final place.
Neither keeper was being called on to perform above and beyond the call of standard duty and defences were definitely winning the night, but the enthusiasm of the crowd did not wane - a crowd that included first team skipper Teddy Sheringham.
The deadlock was finally broken on 62 minutes when, from a Marney free-kick the ball fell loose in the Blackburn penalty area and was met by the boot of Barnard who unleashed a rising drive into the back of the net, giving keeper Kieron Renton no chance.
Galvanised by the goal, three minutes later the lead was doubled after another Marney free-kick from the right.
This time he swung in a low driving cross that was met at the near post by Sutton, who angled a superb diving header past Renton to give the boys a cushion that did not look likely in a tight game.
Blackburn rallied and caused a few anxious moments from crosses, while Barnard collected a yellow card to go with his goal.
Burch had a scare when Blackburn substitute Paul Gallagher knocked the ball out of his hands as he was preparing to take a drop-kick. The referee did not object and the ball dropped just over the bar from the resulting effort with Burch stranded.
Spurs responded minutes later and a rasping Wettner drive was parried away by Renton.
After playing three rounds away, the boys finally discovered the joys of home comforts and a deserved semi-final spot now beckons for Pat's lads.
Team: Burch, Kelly, McKie, Hughes (Bowditch 75), Henry. O'Donoghue, Barnard, Marney, Sutton, Slabber (Galbraith 89), Wettner. Subs not used: Thomas, Rutherford, Herron.
Blackburn: Renton, Cole (Bruce 75), Davey (Black 75), Donnelly, Martin, McEveley, Watt, Nelson, Bell, Johnson (Gallagher 65), Morgan. Subs not used: Drench, Harkins.
By Richard Hubbard
Goals from Lee Barnard and John Sutton saw our Academy under-18 side through to the semi-finals of the FA Youth Cup with a 2-0 victory over a talented Blackburn at the Lane.