Hull's run of defeats came to an end as an equaliser from substitute Sone Aluko secured them a 1-1 draw at Everton.
The Toffees appeared very much in control at half-time of the Premier League contest, going in a goal up thanks to Romelu Lukaku's 34th-minute strike from a Kevin Mirallas cut-back.
But Hull battled back after the break and were level in the 59th minute when Aluko, only just introduced to the action, got past Sylvain Distin and put a nice finish past Tim Howard at his near post.
The Tigers' ex-Everton frontman Nikica Jelavic headed just wide moments later, and the visitors then hung on doggedly for a draw that takes them out of the relegation zone.
Despite being increasingly on top, Everton were still yet to really show a cutting edge, but when Mirallas lashed the ball across the box in the 33rd minute, a flick from Osman brought a diving save out of McGregor.
And moments later, the deadlock was broken as Belgium internationals Mirallas and Lukaku combined for a goal once again, as they had done twice last week when they each scored against Wolfsburg in the Europa League.
Lukaku nodded the ball on for Mirallas, who surged down the right, got the better of Dawson and provided the delivery from which his compatriot rifled home. It was a seventh goal of the season for Lukaku - Everton's £28million club record summer signing - and his third in his last four games.
Diame came off for Aluko, while Leighton Baines had to disappear down the tunnel briefly for treatment on what looked like a bloodied nose.
Besic then looped a shot to McGregor, before Lukaku skewed off-target.
Hull were level when Aluko - six minutes after his introduction - danced past Distin and beat Howard for his first goal since September 2013.