Drama at Ashton Gate late on as Korey Smith broke United hearts and probably scuppered any hopes of Lee Johnson having a glass of red with Jose Mourinho.
The Robins will be joined by Man City, Chelsea and Arsenal in the hat as they continue to dream.
Eden Hazard's magic helped Alvaro Morata deny Bournemouth late on at Stamford Bridge in the other tie tonight.
While Danny Welbeck grabbed the winner in Arsenal's 1-0 win over West Ham last night, and Claudio Bravo was the hero as City defeated Leicester City on penalties.
If the semi-finals live up to the quarters, we're in for a treat!
Find out who will take on who in the two-legged semi-finals below, with the four sides just two games from Wembley.
Carabao Cup draw: Time, date and how to watch
Four teams remain in the competition after this week's round of matches.
Chelsea beat Bournemouth and Bristol City shocked Manchester United to join Manchester City and Arsenal in the semi-finals after they saw off West Ham and Leicester last night.
Carabao Cup: When is the semi-final draw made?
The final four will learn their opponents tonight.
The draw will be made at the end of Bristol City's tie with Manchester United at Ashton Gate.
Carabao Cup draw: How to watch
The semi-final draw will be made live on Sky Sports.
It will be broadcast on Sky Sports Football and Sky Sports Main Event.
It's likely to get underway around 10pm.
Bristol City are in their third EFL Cup semi-final, but have never reached the final
Championship side Bristol City will play Manchester City in the Carabao Cup semi-finals, with Chelsea facing Arsenal in the other tie.
Manchester City and Chelsea will host the first legs in the week beginning 8 January, with the second legs two weeks later.
Bristol City beat holders Manchester United 2-1 to reach the last four.
Manchester City knocked out Leicester on penalties, Chelsea beat Bournemouth 2-1 and Arsenal beat West Ham 1-0.
"It is brilliant," Robins boss Lee Johnson told Sky Sports.
"It's on to another big one against Manchester City over two legs. It is a chance for the players to test themselves against the best players."
Bristol City will look to bridge a huge gulf in resources when they welcome Manchester United to Ashton Gate for tonight's Carabao Cup quarter-final.
City lie third in the Championship, four points outside the automatic promotion places and with their sights fixed on the big time - but the comparison between the two squads spells out the task facing them.
And, while United may not field a first-choice line-up in a competition in which they have typically made changes, City are without a couple of key players in record signing Famara Diedhiou and Republic of Ireland winger Callum O'Dowda.
That leaves defenders Bailey Wright and Hordur Magnusson as the only players with international experience in the Robins' likely line-up - Wright has played 21 times for Australia while Magnusson has recently established himself in Iceland's line-up and has 15 caps.
And without £5.3 million Senegal forward Diedhiou, as well as £1m-plus signing O'Dowda, manager Lee Johnson is likely to choose from a squad of players signed for reported fees totalling around £11.5m.
United full-back Matteo Darmian, signed from Torino for a reported £12.7m in 2015 and with 36 caps for Italy, matches up with City's entire available selection in those two categories.
The 28-year-old is by no means a key man in Jose Mourinho's squad - indeed, it would be possible for Mourinho to select a back five in which Darmian was the cheapest acquisition, with Victor Lindelof, Phil Jones and Marcos Rojo at centre-back and Luke Shaw or Daley Blind on the left.
United's starting XI against Swansea in the previous round counted 272 caps for their countries and cost over £140m to assemble.
The three substitutes used by Mourinho on that occasion - Shaw, Nemanja Matic and Romelu Lukaku - cost as much again and there could be further power to add this time around.
There have been suggestions pre-match that Henrikh Mkhitaryan, signed for a reported £26m from Borussia Dortmund, could be handed an increasingly rare chance to impress and that £89m France star Paul Pogba could feature in midfield having served a three-match suspension.
Zlatan Ibrahimovic is another player thought to be in contention - the striker was signed on a free transfer, but has 116 caps for Sweden and has won league titles in Italy, Spain, France and Holland.
