Leyton Orient 0-1 Hull City
Robbie Brady scored within a minute of coming off the bench as Hull needed extra time to overcome Leyton Orient.
Orient, who had won all five of their previous matches this season, dominated at Brisbane Road and should have led through David Mooney's header.
Orient continued to create the better openings, although Hull's David Meyler had a header cleared off the line.
In the second period of extra time Brady pounced on Liam Rosenior's ball to send Hull into the third round.
With manager Steve Bruce making 11 changes, the Premier League side were not as fluent as Orient who twice went close to taking the lead when Romain Vincelot shot wide from Lloyd James' corner and Kevin Lisbie headed over.
James then forced a save from Hull debutant Steve Harper and the David Mooney drove over from distance.
Mooney squandered the best chance of the opening period when he headed wide from a Dean Cox cross.
The Premier League side finally threatened in the first minute after half time when Meyler met Cameron Stewart's corner and Elliot Omozusi hacked off the line. Cox came close to grabbing victory for Orient in normal time but curled his shot over the bar from the edge of the area.
A minute into the second period of extra time, Brady, who scored the winner in the 1-0 win over Norwich at the weekend, fired in after he got on the end of Rosenior's delivery.
Leyton Orient manager Russell Slade:
"I am very proud of the performance. It was a very good, strong performance.
"I thought there were some nice passages of play, we put them under a lot of pressure whether it was from a corner, throw-in or open play.
"I was pleased, I can't hide that. I couldn't have asked for much more from them, they gave me everything."
Hull manager Steve Bruce:
"Maybe I should have brought [Brady] on 20 minutes earlier and we could have all caught our train home.
"We played them last year in the FA Cup and gave us a run for our money and they have done exactly the same.
"We've made hard work of it. It is simple as that. We are delighted to be in the next round, but they made it very, very difficult. They played very, very well on the night."