When Paul Scholes put United ahead just short of the hour it looked as though it might be the decisive goal in a keenly contested match of few chances.
United surrendered the lead within three minutes as David Thompson scored what could prove an invaluable away goal for Rovers.
After beating United in the Premiership at Ewood Park a little over a fortnight ago, Rovers will be quietly confident of further success.
Rovers manager Graeme Souness said: "We played very well and it would have been unfair not to get anything from the match.
"We had a good night and played some good football and it keeps the tie alive. There is all to play for at Ewood Park."In a low key opening 45 minutes each goalkeeper only had one save to make.
Fabien Barthez did well to keep out a fiercely struck shot from Lucas Neill while in stoppage time Brad Friedel did well to thwart Ruud van Nistelrooy.
Blackburn had a strong appeal for a penalty turned down following a challenge by Mikael Silvestre on Neill and to add insult to injury referee Uriah Rennie booked the Blackburn defender for diving.
Then deep into stoppage time United substitute Ole Gunnar Solskjaer watched in disbelief as his goalbound shot beat Friedel only for 17-year-old defender James McEveley, who has played only three Premiership games, to make a spectacular goal-line clearance as he chested the ball to safety.