Coventry put up a battling second-half performance and were unlucky not to force extra-time in a fast and furious cup tie.
Boro made several changes including the return of leading scorer Yakubu in attack, with Mark Viduka on the bench.
Coventry showed they were prepared to have a go from the start and there was no suggestion of a defensive game and a counter attack policy.
There were loud appeals for a penalty when Yakubu went down the box in the 16th minute but the referee, who was well up with play, turned them down.
Gaizka Mendieta blasted a shot high and wide from 20 yards for Middlesbrough.
The home side took the lead through Jimmy Floyd Hasselbaink after 20 minutes. Yakubu provided a perfect chance for the Dutchman to dart forward, beat goalkeeper Marton Fulop and shoot into an empty net for his ninth goal of the season.
Middlesbrough carried more threat after that and only a fine Fulop save denied Hasselbaink his second goal five minutes later.
Coventry came close to an equaliser through Stern John in the 37th minute.
Mark Schwarzer made a brilliant one-handed save and Emanuel Pogatetz cleared the danger.
Middlesbrough deserved their interval lead but a tactical change by Coventry transformed the second half. The Sky Blues moved Gary McSheffrey into attack in a 4-3-3 formation.
It was a bold gamble to pull the game round and Middlesbrough were forced on the defensive.
There was a possibility at this stage that Middlesbrough might sit back to try and hold on to their lead.
Marcus Hall provided a left-wing cross for John to head wide when challenged by Schwarzer.
Yakubu was well off target for Middlesbrough and it was Coventry who were showing the more attacking enterprise.
Coventry fans were giving their team terrific encouragement and Boro were under the cosh.
Yakubu shot wide in a counter attack and then Mendieta was not far off target with a shot from over 20 yards.
Coventry continued to pile on pressure in a ding-dong battle, while substitute Massimo Maccarone had a clear chance to wrap the game up for the home side in added time.
Maccarone went round Fulop but his angled shot was cleared off the line by Robert Page.