Hull moved two points clear at the top of the Sky Bet Championship after being held to a 0-0 draw by fellow promotion contenders Sheffield Wednesday at the KC Stadium.
The Tigers, held goalless last time at home by another top six side in Brighton, went closest when Sam Clucas struck his shot against the post in the second half.
Wednesday had almost taken the lead in the first period when a long-range shot from Fernando Forestieri came back off the bar.
The Wednesday forward was sent off in stoppage time when he was shown a second yellow card for simulation.
The first effort on target came from Hull’s Curtis Davies after 15 minutes but it was at the wrong end.
The central defender got a foot to a Barry Bannan shot which was going wide and steered it towards his own goal but McGregor was in the right place to block with his leg.
Robert Snodgrass went close shortly after when he controlled a deep cross to the far post but his shot from a tight angle was saved by Keiren Westwood.
McGregor tipped over a free-kick from Forestieri from over 30 yards out which had been awarded when the forward was fouled by Dawson with half an hour gone.
Forestieri went even closer ten minutes before half-time when his dipping shot beat McGregor but came back off the bar.
Abel Hernandez forced Westwood to reach high to palm out his shot from the edge of the area.
Clucas was denied by the post after 65 minutes when he shot from the edge of the area after exchanging passes with Jake Livermore.
The visitors cleared the loose ball for a corner but Davies headed just wide as the home side saw another opportunity go begging.
The Wednesday goalkeeper was brave when he got up to tip the ball away under pressure from substitute Chuba Akpom and then got to the loose ball before Hernandez with ten minutes remaining.
Forestieri was sent off in stoppage time when referee Tim Robinson showed him a second yellow card for simulation when he went down after a Dawson challenge just five minutes after being booked for a foul.