The Foxes could only manage a draw against the Tigers, who were reduced to 10 men midway through the second half after the midfielder was dismissed for tripping Jamie Vardy
Heavy defeats for fellow strugglers QPR and Sunderland meant Nigel Pearson's rock-bottom side could have moved within four points of safety with a win at the King Power Stadium.
However, Pearson - a former Hull boss - witnessed his side fail to break down the visitors, who played the last 18 minutes a man light after Tom Huddlestone was sent off for a second bookable offence.
Hull manager Steve Bruce, who this week signed a new three-year contract at the KC Stadium, saw Nikica Jelavic miss a gilt-edged chance from close range in the first half - the striker failing to sort his feet with the goal gaping.
Huddlestone's dismissal ensured a nervy ending for the visitors but a draw means they stay 15th, having moved six points above the bottom three.
There were few chances of note in a tepid opening, but the visitors should have broken the deadlock in the 20th minute with Jelavic guilty of one the misses of the season.
Huddlestone's superb dinked pass to Ahmed Elmohamady was unselfishly played into the path of the Croatian striker, who got the ball caught under his feet eight yards from goal and he bundled his shot into the hands of a relieved Mark Schwarzer.
Jelavic did have the ball in the back of the net soon after when Schwarzer spilled a high cross, but the whistle had already gone as the veteran goalkeeper was clattered by Dame N'Doye.
The hosts grew into the first half and Riyad Mahrez - who scored Leicester's winner in a 1-0 victory in December's corresponding fixture – played a wonderful teasing cross into the area that Andrej Kramaric should have been braver with, but Alex Bruce's presence put him off.
Michael Dawson made an important block on Esteban Cambiasso as Leicester sought a quick start to the second half and, at the other end, Jelavic saw another good chance go begging from a corner.
At the other end McGregor had to be wise to palm away a mis-hit Vardy cross that was heading for the top right-hand corner.
Leicester hopes were raised in the 72nd minute when Huddlestone was given his marching orders by referee Jon Moss for bundling Vardy to ground just outside the penalty area - the midfielder having already been booked in the first half.
The hosts poured forward and substitute David Nugent flicked wide at the near post, though Abel Hernandez should have stolen the points late on, only to shoot tamely at Schwarzer and deny his manager Bruce a fine end to a good week.