The players, wearing shirts with Black Lives Matter across the back instead of surnames, paused to support the BLM movement at Villa Park and the Etihad Stadium.
There was also a moment's silence before kick-off in memory of those who have died in the coronavirus pandemic.
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"Sheffield United and Aston Villa were proud to stand in solidarity with the actions of the players and coaching staff of both football clubs during the first ten seconds of tonight's Premier League fixture, expressing our collective support for the Black Lives Matter movement," read a joint statement from Villa and the Blades.
"In the first Premier League fixture of Project Restart both clubs hope that the act of 'taking a knee' will send a strong message of unity and amplify the many messages of support from Premier League players and the wider football family.
"The directors of both clubs, Chris Wilder, Dean Smith, Billy Sharp, Jack Grealish and the players of United and Villa are in full support of this action. We believe that 'taking a knee' at the start of the fixture and after the pre-match minute's silence, allowed both clubs to pay their respects to Covid-19 victims and to show the deep gratitude we all feel for our brave and selfless front-line workers."
The kneeling gesture comes amid worldwide protests against racial injustice following the death of George Floyd, a black man who died in police custody in Minneapolis on May 25.
Several Premier League clubs in recent weeks have kneeled to show their support for the cause. Former NFL quarterback Colin Kaepernick popularised the gesture as a way to protest racial issues.
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