The result secures back-to-back Premier League victories for Steve Bruce’s side, the first time Hull have achieved such a feat since October 2008.
Both sides played their part in an entertaining fixture, but the match was settled when Brady was adjudged to have been fouled by Joey O’Brien in the box and he turned the spot-kick home.
James Tomkins had a header cleared on the line, while Jake Livermore went closes to a second for Hull, but he could only hit the post.
And with 15 minutes remaining West Ham had another penalty claim from a Jake Livermore handball turned away.
Steve Bruce welcomed back Maynor Figueroa after the left-back missed the 3-2 win over Newcastle last Saturday for personal reasons, while West Ham made just one change to the team that lost 3-2 to Everton, James Tomkins replacing James Collins at centre-back.
After a bright opening, Hull took the lead in questionable circumstances in the 12th minute.
Ahmed Elmohamady launched a hopeful ball into the box and Brady went down under minimal contact from O’Brien with Kevin Friend awarding the spot-kick to the visitors’ chagrin.
Undeterred by the visitors’ protests, Brady picked himself up to send Jaaskelainen the wrong way.
The goal sparked West Ham into life and James Tomkins saw his header from Matt Jarvis’ corner chested off the line by Elmohamady in the 20th minute. Goal-line technology showed the ball did not cross the line.
Still, the away side pushed forward and Mohamed Diame should have done better when he met Jarvis’ centre but he headed wide from eight yards before missing the ball with a wild swing at another Jarvis cross.
The home side weathered the storm and had several opportunities to extend their advantage before the break.
First, Jaaskelainen made a smart save to his left from a Aluko free-kick, before Curtis Davies saw his header cleared off the line by Modibo Maiga and the Finn had to be alert again from the resulting corner to push Elmohamady’s near-post header wide.
The home side had the ball in the back of the net early in the second half when Aluko turned Tomkins and slotted past Jaaskelainen, but the celebrations were curtailed by the linesman’s flag.
West Ham then had a penalty shout in the 53rd minute when Davies jumped to clear a free-kick and the ball hit his arm as it travelled towards the turf.
The away side were nearly punished further when Danny Graham controlled Tom Huddlestone’s pass before he laid into Livermore whose driven effort rebounded off the post.
West Ham were denied another penalty with 15 minutes remaining when Livermore appeared to use his elbow to clear Ricardo Vaz Te's cross from the left.
And they once more came close to grabbing a point when Ravel Morrison collected a deep cross but he fired his half-volley well over the crossbar.
West Ham nearly got the leveller their second-half play deserved when Vaz Te attempted a spectacular overhead kick from Morrison's cross, but Allan McGregor held safely to secure the points.
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