Romelu Lukaku marked his Everton debut with a dramatic late winner after Leighton Baines produced two brilliant strikes in a 3-2 victory at West Ham on Saturday.
Roberto Martinez's team looked set for their first Premier League defeat of the season when Mark Noble gave West Ham a 2-1 lead with a second half penalty.
But Baines, who had already produced one superb free-kick to cancel out Ravel Morrison's opener, conjured up another stunning set-piece to equalise with seven minutes remaining after Noble was sent off for a second booking.
And that set the stage for Belgian striker Lukaku, on loan from Chelsea, to head in the winner two minutes later.
Everton's second league win of the campaign extended their unbeaten run to five matches, while West Ham slip to 14th place following their fourth successive league game without a victory.
The visitors went close after six minutes when Kevin Mirallas tested Jussi Jaaskelainen and Steven Naismith was inches away from a second attempt when the ball sailed past.
But West Ham, missing injured trio Andy Carroll, Joe Cole and Stewart Downing, ended their 314-minute scoring drought when Morrison fired them ahead in the 31st minute.
Matt Jarvis threaded his way infield and teed up Morrison and the former Manchester United midfielder drilled the ball home via a deflection off Naismith.
However, Lukaku came on for the second half in place of the injured Nikica Jelavic and the powerful forward transformed the match.
His clever early touch was taken on by compatriot Mirallas, who raced to the byline and crossed only for West Ham to recover by getting numbers back.
Everton maintained the pressure and in the 62nd minute the equaliser arrived, Baines steering a terrific 20-yard free-kick beyond Jaaskelainen into the top left corner.
Noble flashed a corner wide of the left post and Baines forced a save from close range as the match opened up.
Sam Allardyce's team moved in front when Noble drove home from the penalty spot after being hacked down by James McCarthy in the 76th minute.
But the West Ham midfielder was sent off by referee Lee Mason in the 82nd minute for bringing down Ross Barkley when he was already on a booking.
And Everton took advantage of their numerical superiority in a thrilling finale.
Baines delivered the equaliser with another brilliant free-kick in the 83rd minute and Lukaku capped his inspirational display with the headed winner from a Mirallas cross with five minutes left.