Anthony Elanga blazed over to send Boro through 8-7 after United's seventh spot-kick defeat in eight contests, although it would no doubt argue the tie should not have advanced to that stage.
🚨 @ManUtd is OUT OF THE #FACup 😱 It went to penalties against @Boro after a 1-1 draw after 120 minutes, and at 7-8 in the shootout, someone had to miss ... Full report soon | #MUNMID pic.twitter.com/EpbZlH8Fb9— beIN SPORTS (@beINSPORTS_AUS) February 4, 2022
Ralf Rangnick might point to generous officiating from Anthony Taylor that did not punish Duncan Watmore's handball in the build-up to Matt Crooks' second-half equaliser for Boro.
But United's inability to add to a lead secured by Jadon Sancho was equally damaging, its 30 shots worth a combined 4.32 expected goals, an early Cristiano Ronaldo penalty among the misses as the Red Devils crashed out.
By the time Sancho made the most of Boro's latest piece of haphazard defending to break the deadlock with a deflected shot across Joe Lumley, United could have been two or three up.
Sancho clipped a delicate attempt on to the crossbar after Lumley spilled a long ball, then Anfernee Dijksteel clumsily brought down Paul Pogba in the box, only for Ronaldo to drag his spot-kick wide. Bruno Fernandes volleyed wildly over when played onside, too.
Chances continued to come and go after the 25th-minute opener, with Marcus Rashford letting Boro off the hook again early in the second half.
That profligacy came back to bite United in bizarre circumstances when Watmore blatantly controlled Isaiah Jones's cross with his hand but directed a lob across the face of goal, allowing Crooks to steal in and net a leveller that the video assistant referee (VAR) did not overturn.
Fernandes pulled a straightforward finish against the foot of the post soon afterwards, failing to prevent an extra time period in which Dean Henderson was required to make a close-range stop from Aaron Connolly to reach the shoot-out.
Each of the first 15 kicks were scored, before Elanga finally failed, stunning the home support, and sending those in Boro colours wild with delight.