Hasselbaink scored for Boro and could have made it two
Jimmy Floyd Hasselbaink's first-half strike took Middlesbrough past Coventry in the FA Cup fourth-round replay.
The Dutch forward rounded Coventry keeper Marton Fulop to slot home his ninth goal of the season after 20 minutes and set up a trip to Preston.
Hasselbaink, 33, could have added to his tally shortly after but Fulop blocked his left-foot volley.
Coventry grew in belief in the second half and went close through Marcus Hall and Stern John but Boro held firm.
The home side were the dominant force in the first period but were unable to make more of their territorial superiority at the Riverside.
Gary McSheffery posed the only real threat for the Championship side down Boro's left flank, and his cross set up John's first chance, forcing a fine save from Mark Schwarzer eight minutes before the break.
The visitors turned the tables early in the second half with a smattering of half-chances before Hall went close with a left-foot shot and John drew a late diving save from Schwarzer.
Yakubu, Spaniard Gaizka Mendieta and Stuart Parnaby all had speculative efforts for Boro, while Massimo Maccarone squandered a one-on-one with Fulop minutes before the end.
Middlesbrough manager Steve McClaren:
"The result was all important - winning football matches puts smiles on people's faces.
"It was a gritty performance - not pretty, but gritty. Being hard to beat and keeping a clean sheet was the most important thing.
"Everybody from the front to the back gave a performance which showed they didn't want to get beat."
Coventry manager Micky Adams:
"We felt it was a good opportunity for us to take advantage of their problems, that was in our favour to some degree.
"But you have to remember they still have quality players, particularly at the business end of the pitch.
"They will kick in and produce a little bit of magic so you have to concentrate for 90 minutes, we had one lapse really."
Middlesbrough: Schwarzer, Pogatetz, Riggott, Southgate, Parnaby, Mendieta (Bates 81), Doriva, Rochemback, Taylor, Yakubu (Maccarone 71), Hasselbaink.
Subs Not Used: Jones, Viduka, Johnson.
Booked: Taylor, Yakubu, Pogatetz.
Goals: Hasselbaink 20.
Coventry: Fulop, Whing (Morrell 85), Page, Williams, Hall, Scowcroft, Hutchison, Doyle, McSheffrey, Adebola, John. Subs Not Used: Ince, Jorgensen, Heath, Shaw.
Booked: Scowcroft, Hutchison.
Ref: M Atkinson (W Yorkshire).