Newcastle's Dutch striker Patrick Kluivert, neatly set up by captain Alan Shearer, coolly finished into the far corner after five minutes of a rousing game at St James' Park.
Striker Paul Dickov converted an 83rd minute penalty to give Blackburn a scrappy victory over his old club, securing their first appearance in the last four since 1960.
The winning teams joined holders Manchester United, who thrashed Southampton 4-0 in their quarter-final on Saturday, and Arsenal, who beat Bolton Wanderers 1-0, in Monday's draw.
Sunday's spotlight was trained firmly on Tyneside, where an early header by Kluivert had secured a 1-0 win over runaway Premier League leaders Chelsea in the previous round.
This time, Kluivert side-footed past England goalkeeper Paul Robinson from eight metres for his 11th goal of the season and Newcastle's seventh consecutive victory.
The breakthrough followed good work by Shearer who made the most of poor defending by Ledley King when he pulled the ball back to Kluivert to deliver the finishing touch.
Despite the setback, Martin Jol's visitors retained their composure and enjoyed plenty of possession, but were unable to translate that supremacy into goals -- due mainly to an inspired display by Newcastle keeper Shay Given.
Graeme Souness, who left Blackburn to become Newcastle's manager last September, said: "We played well in the first 15 minutes and then Tottenham took over the game.
"They'll feel that Lady Luck's not been with them, Shay's made a couple of good saves, but we've missed a couple of chances on the break towards the end to have killed it."
As for their next opponents, Souness said: "I'd love to be playing Blackburn
Dutchman Jol was more disappointed with referee Rob Styles than with his team, saying: "I learned a nice phrase when I came over here -- 'you win some, you lose some'.
"But I don't think we could win anything today with this man in black."
Spurs recovered well from conceding the early goal, striker Frederic Kanoute having a low shot saved by Given and then putting a close range effort wide, while the Newcastle keeper also denied Jermain Defoe.
Newcastle's cause was undermined five minutes before the break when centre half Titus Bramble limped off with an injury that will keep him out for several weeks and midfielder Jermaine Jenas ended up in the unfamiliar position of left back.
Tottenham pushed their hosts onto the back foot for much of the second half but were unable to find a way past Given, who pulled off one astonishing double-save.
GIVEN DOUBLE
After Kanoute eluded Jenas on the by-line, Given repelled a first-time shot from international team mate Robbie Keane and then reacted brilliantly to push aside Defoe's rising shot.
The industrious Kieron Dyer squandered a late chance to double Newcastle's lead in the final minute, while Aaron Hughes cleared a Kanoute effort off the line at the other end.
In a frenetic closing period, Newcastle's substitute striker Shola Ameobi also fluffed a good opening and Tottenham had loud appeals for a penalty waved away.
Blackburn were heading for a replay against Leicester until Norwegian midfielder Morten Gamst Pedersen was felled by defender Darren Kenton and Dickov blasted home the spot-kick in the 83rd minute at Ewood Park.
Next month's semi-finals, along with the final on May 21, will all be played at Cardiff's Millennium Stadium.
