Cenk Tosun scored for the second successive fixture as Everton ended Brighton & Hove Albion’s five-match unbeaten run.
Sam Allardyce’s team had the better first-half chances but had to wait until the hour mark for a breakthrough.
Gaetan Bong deflected Yannick Bolasie’s cross into his own net under pressure from Theo Walcott.
On 76 minutes, Tosun made it 2-0, firing in off the bar from Leighton Baines's pass.
Brighton’s task got harder when Anthony Knockaert was shown a red card on 80 minutes for a dangerous challenge on Baines.
Mat Ryan stopped a third Everton goal by saving Wayne Rooney’s penalty.
Everton climb to ninth, on 37 points, three above Brighton, who slip to 11th.
Everton: 17 Mar v Stoke City (A)
Brighton: 31 Mar v Leicester (H)