Steve Bruce was relieved to still be in the FA Cup after Hull were given another fright by Leyton Orient.
League One Orient were only a minute from causing an upset in Humberside 10 days ago, and rattled the Premier League hopefuls with a freak late equaliser from Dean Cox to take the replay to extra-time.
But Tom Cairney struck with three minutes remaining to secure a 2-1 win and an all-Yorkshire tie with Barnsley in round four.
"All credit to Orient, they have given us two really difficult games and if we're honest we could be out of the cup. But we're not," said Tigers boss Bruce.
"We had some good chances to put the game to bed, but when it's just 1-0 you are always on edge and they've scored with the last kick, really, to take it to extra time. And then it's anybody's game.
"You hope a little bit of quality comes through in the end but fair play to Orient, they took us to two really hard cup ties and on another day could have gone through."
Nick Proschwitz had denied Orient victory in the original tie and the German striker, who has been something of a let-down in the league for Hull, showed his liking for the cup again with a stunning opening goal before half-time.
The £2.5million summer signing flicked up Liam Rosenior's cross with his first touch before swivelling and rifling a 20-yard volley past Jones with his second.
Orient had a David Mooney goal disallowed in the first half and one from Lee Cook chalked off in the second.
But Cox conjured up a bizarre equaliser in the 87th minute when his cross flew over Hull goalkeeper Eldin Jakupovic and straight into the net.
However, Hull had the last word in extra time when Orient could only clear Proschwitz's cross to the edge of the area and Cairney fired it back past Jamie Jones.
Orient boss Russell Slade was adamant Cook's goal should have stood.
"I've just seen it and it's two yards onside," he stormed.
"We've done more than enough over the two games to get a result so that just frustrates me even more.
"You want the officials to get it right on the night. You can't have that, it's a massive game for this football club and someone is not doing their job."