It was sweet revenge for the humiliating 6-1 defeat they suffered at the hands of Hull earlier this season and was their first win under new manager Garry Monk.
Showing great determination to improve their precarious position, Birmingham were impressive winners as they chalked up their best victory of the season, Jota's first two goals at St Andrew's sandwiching a Che Adams cross which sailed straight in.
Birmingham, who remain in the bottom three despite the result, could have recorded an even more clear-cut victory but for the brilliance of goalkeeper Allan McGregor, who defied the home side with a string of excellent saves in the first half.
Following their recent impressive form which had taken them nine points clear of the relegation zone, Hull were very disappointing as they were given little scope to excel by a Birmingham side fighting for their lives.
Playing in a blizzard, Birmingham were determined to get on the front foot and only a brave save by McGregor, who had to race to the edge of his area, prevented Adams opening his account.
Birmingham were not put off by the Baltic conditions as they continued to launch a series of attacks, with Hull's defence often stretched to the limit.
They were exposed in the 12th minute when Adams broke clear down the right and produced a perfect low cross which Jota converted at the near post.
Birmingham's fans had waited a long time to see Jota get on the scoresheet as this was his first at St Andrew's since his record signing from Brentford last summer, his only previous goals for the club being a double at Sheffield Wednesday last month.
Sterling work by skipper Michael Dawson and Ondrej Mazuch kept Hull in the game and Harry Wilson displayed the Tigers' potential danger with a rasping left-footed shot which whistled low past the far post.
Hull were again indebted to the skill of McGregor, though, with two saves in quick succession to deny the impressive Adams as the Scotland international emerged as the Tigers' star man.
Adams, however, finally enjoyed some success three minutes into the second half. He outpaced Dawson but then ran out of space, turned back on himself and produced a hopeful high lob which, to his own surprise, went over the head of McGregor and into the far top corner of the net.
Birmingham were unrecognisable from the team which has struggled badly this season and they completed their belated success when Jota collected a loose ball to fire home the third goal in the 59th minute.
Tigers manager Nigel Adkins was far from happy with the outcome.
He said: “I will have to take a bit of time to reflect on this result.
“We certainly didn’t see this result coming. We had focused the players’ minds as we knew that it would be a tough game, as it proved to be.
“We had enjoyed two good victories and we thought we would be a threat going forward with Abel Hernandez back in the side.
“We were on the back foot from the start of game, while Allan McGregor was excellent. He kept us in game in the first half with some really good saves.
“The first half was as bad as we have played since I came in as manager. Credit to Birmingham, they deserved to win and we didn’t.
“We were second best and now we have two big games against Aston Villa and Wolves.”