Elsewhere, Aston Villa lost to Fulham in Portugal, Paul Clement’s first game in charge of Derby ended in a defeat at Grimsby and Blackpool’s clash at Lancaster City was abandoned after supporters invaded the pitch.
Meanwhile, Southampton lost twice in Austria and there were injury blows for both Middlesbrough and Blackburn.
Peterborough 3-3 West Ham
Slaven Bilic’s first full game in charge of West Ham ended in a 3-3 draw against Peterborough at London Road.
Ricardo Santos headed the home side into a 10th-minute lead, but Mark Noble (12) and Diafra Sakho (13) put West Ham 2-1 ahead before youngster Martin Samuelsen extended their lead in the 23rd minute.
Peterborough fought back as Jon Taylor rounded Adrian to score before the break and Michael Bostwick levelled from the spot after Noble upended Marcus Maddison in the box.
Barnet 3-5 Crystal Palace
Dwight Gayle scored a hat-trick as Crystal Palace beat Barnet 5-3 at The Hive.
Alan Pardew did not take any of his international players – including record signing Yohan Cabaye – to the club’s first pre-season friendly match but Gayle impressed with three goals in the first 51 minutes of the game.
Barnet had taken the lead through John Akinde in the first minute and Luke Gambin and Kevin Lisbie scored in the second half, but goals from Reise Allassani and Fraizer Campell secured the victory for the Premier League side.
Aston Villa 1-3 Fulham
Christian Benteke was an unused substitute for Aston Villa as they lost 3-1 to Fulham in a friendly played in Albufeira in Portugal.
Matt Smith headed Fulham in front on his return to the club after a loan spell at Bristol City last season, but substitute Libor Kozak levelled from close range 10 minutes after the interval.
Villa boss Tim Sherwood made 10 changes at half-time, but Liverpool target Benteke was not one of them and watched on as Alexander Kacaniklic’s stunning 25-yard strike in the 67th minute and Ross McCormack’s composed finish three minutes from time settled the game.
Swindon 0-4 Everton
A strong Everton side kicked off their pre-season campaign in convincing fashion with a 4-0 victory over Swindon at the County Ground.
Kevin Mirallas scored a quick-fire brace shortly after half-time, before Romelu Lukaku added a third in the 88th minute.
Impressive youngster Conor McAleny, who had set up Lukaku, added a fourth for Everton in stoppage time.
AFC Wimbledon 2-2 Watford
George Francomb’s stoppage-time penalty earned AFC Wimbledon a 2-2 draw with Watford at the Cherry Red Records Stadium.
The Sky Bet League Two side had taken the lead through a Callum Kennedy penalty from the spot, but Watford went in front with goals from Odion Ighalo and Fernando Forestieri either side of the break.
The late goal means that the two clubs will share the Football Manager Trophy, named after the shirt sponsor of both clubs.
Gorleston 0-7 Norwich
Cameron Jerome scored a first-half hat-trick as Norwich started their pre-season campaign in style with a 7-0 win at Gorleston.
Tony Andreu and Vadis Odjidja-Ofoe also netted before half-time, at which point manager Alex Neil made 11 changes to his team.
Lewis Grabban and Jonny Howson scored for the new-look Norwich team as they completed the rout after the break.
Southampton fourth in Audi Quattro Cup
Ronald Koeman’s men lost twice in Austria, firstly going down 1-0 to La Liga side Valencia in their semi-final after a close-range strike from Argentine winger Pablo Piatti.
And then, with games lasting for only 45 minutes, the Saints went down 2-0 to Red Bull Salzburg in their third-fourth place playoff, with Havard Nielsen and Dimitri Oberlin scoring the goals for the hosts.
Grimsby 2-1 Derby
Paul Clement’s first game in charge of Derby ended in disappointment as they were beaten 2-1 away at Grimsby.
Padraig Amond opened the scoring with a close-range finish in the 24th minute and Craig Clay doubled the advantage three minutes later.
Johnny Russell scored with a free-kick for Derby three minutes after the break, but the away side were unable to give their manager a winning start.
Lancaster City A-A Blackpool
Blackpool’s clash at Lancaster City was abandoned in the second half after a number of fans invaded the pitch.
In scenes reminiscent of the final game of last season against Huddersfield, around two dozen supporters took to the pitch to protest against chairman Karl Oyston and boss Neil McDonald took the players off the field.
Blackpool were winning 3-1 at the time thanks to a brace from Mark Cullen and a tap-in from Henry Cameron. Ryan Winder had equalised with a penalty for Lancaster in the 23rd minute.
The best of the rest
Dean Furman and Craig Conway were on target for Blackburn as they won 2-0 at Accrington Stanley but the game was marred by an injury to Jordan Rhodes.
The Blackburn striker was taken off on a stretcher during the first half and reappeared on crutches after the interval.
Middlesbrough also suffered a major injury blow as they won 1-0 away at York City.
Bradley Fewster scored the only goal of the game in the 79th minute, but new signing Alex Baptiste was taken off during the first half of his debut after suffering a suspected broken leg.
Elsewhere, Niall Heaton’s 72nd-minute equaliser cancelled out Sergiu Bus’s 49th-minute goal as Alfreton held Championship side Sheffield Wednesday to a 1-1 draw.