Match ends, West Bromwich Albion 1, Everton 2.
Gareth Barry's close-range header secured Ronald Koeman's first victory as Everton manager as they came from a goal down to win at West Brom.
The home side went in front inside 10 minutes as Gareth McAuley headed in a Craig Gardner corner at the far post.
Everton carried more threat once Romelu Lukaku came on as a first-half substitute, and Kevin Mirallas rolled in an equaliser just before the break.
Barry then forced the ball in after Mason Holgate's touch from a corner.
Lukaku stays - and proves pivotal
Koeman said after the match that Lukaku would be staying at Everton - good news for Everton fans concerned that the striker may return to former club Chelsea.
The Belgium international, bought by Everton for a club-record £28m from Chelsea in 2014, was his team's top scorer last season, and his power up front played a significant part in turning the game around.
Koeman's team were flailing in attack for much of the first half, with the 5ft 9in stature of Gerard Deulofeu proving little match for Albion's 6ft 5in centre-half Jonas Olsson.
Lukaku, still straining for fitness after a recent heel problem, was thrown on to give Olsson a rougher time, with Deulofeu switched to the right flank. It worked, even though the Belgian did not score himself.
Everton, who dominated possession throughout, began to create more openings - and made them count. Lukaku passed up a great late chance to make sure of victory, as he was denied by a fine Ben Foster save, but his job was done.
Albion succeed and fall with the set-piece
Before kick-off Koeman was asked in a television interview if he had made special plans to counter West Brom's threat from set-pieces. He said that he had not.
When McAuley headed in Gardner's corner early on, it looked as if Everton would pay for that approach.
It certainly raised hopes for Guochuan Lai, the Chinese businessman who led a takeover at Albion earlier this month, and who was watching his new club in person for the first time.
Albion were managing to make life uncomfortable for Everton's three-man central defence, despite having only around a third of the possession.
Yet if the loss of a goal seconds before half-time knocked the home side off their stride, it was the manner of Everton's second that was something of a surprise.
Head coach Tony Pulis prides himself on having well-drilled teams, yet they were caught out defensively from a corner, with Barry getting free of his markers to turn in a loose ball that should have been dealt with.
Strength in depth lets Everton mix and match
Pulis expressed concerns before the match about the strength of Everton's bench - which included Lukaku, Yannick Bolasie and Ashley Williams.
"It's a top-six bench," said the West Brom coach, who has struggled to strengthen his own squad during the summer, bringing in only winger Matt Phillips from QPR for £5.5m.
The fact that Koeman had options in reserve undoubtedly helped. Winger Bolasie, signed from Crystal Palace during the week, was excellent after coming on, racing past Jonny Evans down the right to deliver a cross that Ross Barkley somehow headed wide with under 20 minutes to go.
Yet Everton's willingness to mix up their approach - not always the case when they played a possession-based game under Roberto Martinez last season - was also a factor in changing the game.
Their equaliser was straight out of the Martinez playbook, with Barry and Barkley exchanging quick passes to feed Mirallas, whose shot had just enough on it to beat Ben Foster.
Yet they were prepared to go direct to Lukaku when needed, and carried a threat at set-pieces, with Foster reacting well to save Ramiro Funes Mori's header from a free-kick seconds before Barry's winner.
Man of the match - Gareth Barry (Everton)
The stats you need to know
- West Brom have gone five home games without a win in the Premier League (D1 L4) for the first time since December 2014
- Everton have kept just one clean sheet in their last eight away games in the league
- Since the start of the 2012-13 season, no defender has scored more Premier League headed goals than Gareth McAuley (eight, along with John Terry)
- Kevin Mirallas has scored three goals in his last five league games; as many as in his previous 25 beforehand
- Mirallas has scored in each of his last three Premier League games at The Hawthorns
- Gareth Barry scored his first away goal in the Premier League since August 2011 (for Manchester City against Bolton)
- Everton fielded their first unchanged line-up in the Premier League since February 2016 (also against West Bromwich Albion)
The EFL Cup is next up for both teams on Tuesday: Everton host League Two side Yeovil, while West Brom go to Northampton, of League One.
- 3OlssonBooked at 59mins
- 6EvansBooked at 90mins
- 10PhillipsSubstituted forLekoat 65'minutes
- 8GardnerSubstituted forMcCleanat 64'minutes
- 18BerahinoBooked at 26minsSubstituted forLambertat 78'minutes
- 22StekelenburgBooked at 90mins
- 25Funes Mori
- 16McCarthySubstituted forLukakuat 38'minutes
- 11MirallasSubstituted forWilliamsat 81'minutes
- 7DeulofeuSubstituted forBolasieat 61'minutes
- Neil Swarbrick
- Shots on Target
Second Half ends, West Bromwich Albion 1, Everton 2.
Attempt missed. Ben Foster (West Bromwich Albion) right footed shot from outside the box is close, but misses to the right following a set piece situation.
Hand ball by Mason Holgate (Everton).
Jonny Evans (West Bromwich Albion) is shown the yellow card for a bad foul.
Yannick Bolasie (Everton) wins a free kick in the defensive half.
Foul by Jonny Evans (West Bromwich Albion).
Attempt saved. Romelu Lukaku (Everton) right footed shot from a difficult angle on the right is saved in the bottom left corner. Assisted by Ross Barkley.
Maarten Stekelenburg (Everton) is shown the yellow card.
Corner, West Bromwich Albion. Conceded by Leighton Baines.
Attempt blocked. Rickie Lambert (West Bromwich Albion) right footed shot from the centre of the box is blocked. Assisted by James McClean.
Attempt saved. Romelu Lukaku (Everton) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Yannick Bolasie.
Foul by Mason Holgate (Everton).
Gareth McAuley (West Bromwich Albion) wins a free kick in the defensive half.
Attempt missed. Salomón Rondón (West Bromwich Albion) left footed shot from the centre of the box is too high. Assisted by Rickie Lambert with a headed pass following a corner.
Corner, West Bromwich Albion. Conceded by Romelu Lukaku.
Corner, West Bromwich Albion. Conceded by Mason Holgate.
Ross Barkley (Everton) wins a free kick in the defensive half.
Foul by Rickie Lambert (West Bromwich Albion).
Phil Jagielka (Everton) wins a free kick in the attacking half.