With next Sunday's semi-final first leg in mind, manager Nigel Pearson rested seven players from a side which won at Preston last week.
Matt Fryatt came off the bench to feature for the first time since breaking his jaw in February.
Yann Kermorgant gave City the lead just before the break with Richie Wellens wrapping up the win from the penalty spot five minutes from the end.
Both sides began brightly with Boro's Scott McDonald firing Julio Arca's knock down wide and James Vaughan just failing to connect with a Paul Gallagher cross before Bradley Jones reacted smartly to deny Gallagher.
Jones then kept out a Jack Hobbs close-range header after Gallagher had nodded on a Nolberto Solano cross with Kermorgant heading the resultant corner from Gallagher just wide.
City were in front on 41 minutes when Kermorgant took a return pass from Gallagher before curling home a superb shot from 25 yards for his first goal for the club.
Vaughan missed a chance to double City's advantage on 55 minutes after he was put clean through by Kermorgant.
Jones blocked the Everton loanee's first shot with the keeper recovering well to keep out Vaughan's follow up.
Jones rescued Boro again soon after with a fingertip save to keep out a long range drive from Dany N'Guessan.
The Seasiders went close on 68 minutes when Justin Hoyte saw his 20-yard drive tipped onto the bar by Conrad Logan.
Boro then squandered a lifeline on 70 minutes when Wellens was ruled to have handled a cross by Arca with Logan diving to his right to keep out Chris Killen's spot-kick.
Logan, in his first start of the season, continued to defy the Teessiders when at full stretch to tip over a 20-yard drive from O'Neil.
Jones was then shown a straight red card on 84 minutes after he had raced from his line to barge over substitute Lloyd Dyer who had been put clean through by Jay Spearing.
Wellens stepped up to chip the resultant penalty down the middle with substitute keeper Danny Coyne diving the wrong way.