A goal by Sergio Aguero gave Manchester City a 1-0 victory against neighbours Manchester United, who played with 10 men for more than 50 minutes.
Defender Chris Smalling was sent off seven minutes before half-time for two yellow cards and in the 63rd minute Aguero scored from a pass by Gael Clichy.
City seemed at that stage to be well on top but United suddenly revived to push them all the way without being able to find an equalising goal at the Etihad Stadium.
Later, Harry Kane's last-minute winner capped a late comeback by Tottenham in a 2-1 victory over 10-man Aston Villa that condemned the home side to a sixth straight loss in the Premier League.
Down to 10 men after Christian Benteke's straight red card in the 65th minute, Villa conceded an equaliser in the 84th through Nacer Chadli before substitute Kane fired in a free kick that deflected off the wall and into the corner.
Tottenham moved up to eighth, with the defeat leaving Villa two points off the bottom three.
10 Sergio Aguero (Manchester City)
9 Diego Costa (Chelsea)
7 Alexis Sanchez (Arsenal)
Saido Berahino (West Bromwich Albion)