This far from convincing victory means McClaren's side continue to flout conventional wisdom. Their Premiership travails mean they can concentrate on the cups. For the second round running, they saw off spirited opposition from the Midlands courtesy of a sparsely attended replay.
While McClaren has presided over one victory in 11 League games, his troops prosper when it comes to sudden-death matches. Stuttgart await in the last 32 of the Uefa Cup, while a first-half goal from Jimmy Floyd Hasselbaink sealed passage to the fifth round of the FA Cup, where they will tackle another Championship side, Preston North End, at Deepdale a week on Saturday.
Like the non-Leaguers Nuneaton in the third round, Coventry exposed Middlesbrough's defensive frailties but lacked the ruthless streak required to cause a shock, although it took a fine Mark Schwarzer save at the death to stop Stern John's long-range effort from taking the tie into extra time.
McClaren said: "It was gritty rather than pretty but we just got back to basics by keeping a clean sheet. I got performances out of my senior professionals and I'm pleased for my players. They have come in for a lot of criticism and they have responded.
"Each time you grind out a result you think this could be the start of something. Now we've got to make sure we don't go from elation to deflation again."
Hasselbaink's goal quickly diminished the prospect of a repeat of the one-man protest in front of the dug-outs endured by McClaren during last week's meeting with Aston Villa.
Coventry were without Dennis Wise, the talisman of three successive League victories, due to a stomach strain, but they coped comfortably until Hasselbaink struck on 20 minutes to stymie the first rumblings of discontent in a sparse crowd of 14,131.
Coventry's ponderous offside trap allowed Hasselbaink to scurry on to an Aiyegbeni Yakubu pass. There was still plenty for the Dutchman to do, but he rounded Marton Fulop to stroke the ball home for his ninth goal of the season.
John then narrowly failed to apply a touch to Andy Whing's low cross and Schwarzer kept out the striker's point-blank header shortly before the break. "There wasn't a lot in it over the two games," insisted Micky Adams, the Coventry manager. "We can be proud despite going out."
Boro's substitute Massimo Maccarone should have doubled the winning margin when, in injury time, he sprinted from halfway to meet Hasselbaink's pass. The Italian rounded Fulop but delayed sufficiently to allow Robert Page to clear the ball off the line. A second goal would have been grossly unfair to the visitors.
Middlesbrough (3-5-2): Schwarzer; Riggott, Southgate, Pogatetz; Parnaby, Mendieta (Bates, 81), Doriva, Rochemback, Taylor; Yakubu (Maccarone, 71), Hasselbaink. Substitutes not used: Jones (gk), Viduka, Johnson.
Coventry: (4-4-2): Fulop; Whing (Morrell, 85), Page, Williams, Hall; Scowcroft, Doyle, Hutchison, McSheffrey; John, Adebola. Substitutes not used: Ince (gk), Jorgensen, Heath, Shaw.
Referee: M Atkinson (Yorkshire).