It was the Newcastle ship which sailed into the fifth round on the back of three goals in the space of 15 minutes of a match they dominated from start to finish.
The Magpies went close several times before finally grabbing goals from Alan Shearer and Shola Ameobi - and each time Coventry had themselves to blame.
Richard Duffy allowed Jermaine Jenas to rob him on the right touchline in the Newcastle half.
Jenas then promptly raced 50 yards into the Coventry box before squaring for Shearer to control and drive a low 17-yard shot across Luke Steele into the left corner.
Five minutes later a Titus Bramble pass appeared to be drifting out of play 35 yards out on the Coventry left.
Full-back Stuart Giddings allowed Ameobi to keep the ball in play and leave him stranded with some sharp footwork before moving into the box and beating Steele from 16 yards with a low shot inside the near post.
Coventry had little joy upfront and did not trouble Newcastle keeper Steve Harper.
But after taking 43 minutes to win a corner, City then earned three in four minutes and from the last of them pulled a goal back in first-half injury time.
Substitute Dele Adebola rose to meet Stephen Hughes' right-wing flag kick to plant a seven-yard header over the top of Stephen Carr on the post.
But hope flickered only briefly for the Sky Blues and new boss Micky Adams as United left-back Celestine Babayaro struck his first goal for the club.
The former Chelsea man left Duffy and Michael Doyle for dead on the left corner of the area before crashing in an angled shot which took a slight deflection on its way past Steele.
It was just rewards for Newcastle who could have easily been out of sight in the first 20 minutes.
Coventry had been hit by a second minute injury to former Newcastle University student Andy Morrell.
Adebola came on in his place as City reshuffled but no combination could stop Newcastle.
Patrick Kluivert miscued a great chance and Babayaro was denied from 25 yards by Steele, who also made a magnificent diving save to keep out a Jenas header.
New singing Amdy Faye was a dominant presence in the middle of the pack, patrolling the midfield expertly and spraying the ball about with accuracy.
Coventry strikers Stern John and Gary McSheffrey, who scored a Youth Cup semi-final hat-trick in 1999, had little or nothing to feed off.
And United were able to see out the final 40 minutes in comfort, while Kluivert should have scored number four on the hour when he volleyed a Shearer cross against the ball from only three yards.
Kieron Dyer and Shearer brought fine saves from Steele as Newcastle retained in full control and, although Adams made a double substitution 11 minutes from time in a vain bid to turn the tide, the match was beyond Coventry and Harper made no saves throughout the 90 minutes.
MAN OF THE MATCH: Amdy Faye (Newcastle): Added a vital extra factor to the Newcastle midfield by confidently breaking up Coventry moves and launching numerous Newcastle attacks.