West Bromwich Albion 1 Everton 2
Everton registered their first win of the campaign thanks to second-half goals from Leon Osman and Ayegbeni Yakubu.
David Moyes' side looked to be suffering a hangover from their last-gasp defeat by Blackburn against an Albion side who played some fluent football.
But the Baggies lacked the killer touch - bar a late penalty from Roman Bednar - and were given a taste of the harsh realities of Barclays Premier League football as the Toffees took advantage of the few chances that came their way.
Baggies boss Tony Mowbray again opted to play only the one out-and-out striker in Ishmael Miller and they failed to create many chances.
But they were still able to pin the visitors back for long periods until Everton play-maker Mikel Arteta started to impose his class on proceedings.
Albion will need to find that firepower if they are to survive but on this performance Everton have still to reach their best.
The first half saw Albion showing virtually all the attacking intent in their first home game in the top flight since being relegated at the end of the 2005-2006 campaign.
Joseph Yobo had to head clear a whipped-in cross from Robert Koren after he was found in space by debutant Gianni Zuiverloon who had been on Olympic duty with Holland.
Baggies defender Abdoulaye Meite won an aerial challenge just outside the Toffees box but he failed to make proper contact with his volley which flew harmlessly wide.
Predictably Joleon Lescott was booed everytime he touched the ball by the home fans because of his one-time connections with Wolves.
Do-heon Kim was not too far off target with a dipping 25 yard free-kick and Everton keeper Tim Howard produced the first save of note after 18 minutes when he went down low to his right to turn a Koren effort around the post.
Everton looked ineffective and Yakubu vented his anger at Lescott after he misdirected one floated pass straight through to Carson.
Albion continued to press and Leighton Baines did well to block an effort from James Morrison after he had wriggled into the box.
Koren was not too far wide with a low drive and Chris Brunt cut in from the left flank and was only inches too high with a dipping drive from fully 30 yards out.
Osman became the first player to be yellow-carded by referee Rob Styles after 38 minutes for bringing down Koren.
Meite was booked in first half injury-time for bringing down Osman and then Zuiverloon followed him into the notebook for disputing the decision.
Albion began the second half in the same vein as the first - on the attack - and Everton boss David Moyes must have been hoping for a big improvement from his side. But there were few signs of it in the opening minutes with Howard twice called into action. He was well positioned to cling on to a fierce rising left-footed drive from Miller.
But the American keeper had to react quickly to come off his line to deny Miller after he had attempted to lob him following good play by Brunt.
Moyes made his first substitution after 58 minutes, bringing on James Vaughan in place of Baxter but Everton were pinned back deep in their own half. Then against the run of play they went ahead after 65 minutes through Osman.
Immediately before that Jack Rodwell had a header from an Arteta corner disallowed for what looked like a push on Paul Robinson. But Arteta was not to de denied and within 60 seconds he had played the ball into the path of Osman who drilled a low shot across Scott Carson into the corner of the net.
Albion were stunned and Brunt was yellow carded for chopping down Arteta.
Mowbray responded by bringing on Bednar and Sherjill MacDonald in place of the impressive but tiring Koren and Kim.
Osman came close to doubling Everton's lead with a volley from 20 yards which was only a foot too high. Then a mix-up between Carson and Meite allowed Yakubu to nip in and head the second goal with 14 minutes remaining.
Bednar converted an 89th-minute penalty after Phil Neville handled but Everton held on for the three points.
Albion manager Tony Mowbray refused to be downcast, after his side's second successive league defeat. He said: "There was plenty of good play from us. We controlled things for the vast amount of time.
"The team looked as if it could go on and win, but in a five-minute spell we conceded two goals. Maybe that is the difference at this level.
"We have got to learn very quickly but we showed we can compete in this league. We showed we should have no fears of the Premier League, because we will be a decent side."
West Brom: Carson, Zuiverloon, Meite, Barnett, Robinson, Morrison, Kim (MacDonald 71), Koren (Bednar 70), Greening, Brunt, Miller (Beattie 80). Subs Not Used: Kiely, Hoefkens, Cech, Pele.
Booked: Zuiverloon, Meite, Brunt.
Goals: Bednar 89 pen.
Everton: Howard, Neville, Yobo, Lescott, Baines, Jagielka, Arteta, Rodwell, Osman, Baxter (Vaughan 58), Yakubu (Nuno Valente 86).
Subs Not Used: Turner, Jutkiewicz, Agard, Kissock, Wallace.
Goals: Osman 65, Yakubu 76.
Ref: Rob Styles (Hampshire).