Middlesbrough could afford to leave top-scorer Jimmy Floyd Hasselbaink on the bench as they eased past Coventry.
Boro went ahead after some comical defending eventually saw Szilard Nemeth tap home a simple chance from close in.
And they doubled the lead when keeper Luke Steele missed Colin Cooper's cross and James Morrison nodded home.
Andy Morrell had the visitors' best chance but headed over and home sub Danny Graham raced through to wrap up the win with 20 minutes to go.
Middlesbrough boss Steve McClaren made nine changes from the team which started Sunday's Premiership game against Portsmouth.
But the holders went ahead after just four minutes when Stuart Downing's rising
shot was flapped at by keeper Steele.
Dean Leacock's dismal attempts to play a backpass let in Nemeth, who knocked
home the simplest of chances.
Coventry responded through Morrell's flick into the Boro box which just failed to reach Eddie Johnson and was cleared by Cooper.
Boro increased their lead in the 24th minute when Steele missed Cooper's ball in from the left, allowing Morrison to nod home.
McClaren opted to withdraw Downing at half-time and give 19-year-old Graham only his second senior appearance.
Coventry finally fashioned a chance on target just past the hour when Stephen Hughes' low drive was held by Carlo Nash.
Two minutes later Nash got down well to hold substitute Patrick Suffo's free-kick on the goal-line.
Graham grabbed Boro's third in the 70th minute, collecting Doriva's pass from the right and shooting home low past Steele from the edge of the box.
Fellow substitute Tony McMahon came close to grabbing a fourth with two minutes to go when his shot from the right beat Steele but hit the post.
Middlesbrough: Nash, Davies, Ehiogu, Riggott, Cooper, Morrison, Doriva, Wilson, Downing (Graham 45), Nemeth, Job (McMahon 64). Subs Not Used: Jones, Parlour, Hasselbaink.
Goals: Nemeth 4, Morrison 25, Graham 70.
Coventry: Steele, Carey, Leacock, Shaw (Whing 81), Giddings, Gudjonsson (Suffo 58), Hughes, Deloumeaux, Doyle, Morrell, Johnson (McSheffrey 71).
Subs Not Used: Shearer, Pead.
Ref: U Rennie (S Yorkshire).