Everton were beaten 4-3 by Real Betis on penalties in the Dresden Cup on a day when Andre Gray stepped up his preparations for life in the Premier League with a pre-season hat-trick against Rangers.
Conor Grant and Kieran Dowell both missed in the shoot-out for Ronald Koeman's side, who had been gifted the lead in normal time by an Aissa Mandi own-goal ahead of German Pezzella's equaliser.
Sunderland were also held to a 1-1 draw in their friendly against Montpellier, Fabio Borini putting the English side ahead in Aix-les-Bains only for Souleymane Camara to level.
Charlie Austin's late header proved enough to seal victory for Southampton over Groningen, who had Hans Hateboer sent off seven minutes before the break.
Bournemouth also earned a 1-0 success, club-record signing Jordon Ibe curling home what proved to be the winner against Cardiff City after only 12 minutes.
There was better news for Cardiff's arch-rivals Swansea City, for whom winger Wayne Routledge scored twice in a 4-0 win at Wolves, with the home side seemingly doing little to impress new boss Walter Zenga as he watched on from the stands.
New signings Alvaro Negredo and Viktor Fischer were both on target as Middlesbrough beat Aston Villa 3-1 at Villa Park, while Gray netted a treble as Burnley won by the same scoreline at Rangers.
Elsewhere, there were defeats for top-flight duo Crystal Palace and Watford at Fulham and QPR respectively.
Sone Aluko, Matt Smith and Floyd Ayite all found the net for Fulham in their 3-1 win, while Northern Ireland international Conor Washington scored the second of QPR's goals as they ran out 2-0 victors at Loftus Road.
A brace from Norway international Adama Diomande saw Hull City edge out Nottingham Forest 2-1, while West Brom were held to a 0-0 draw by League Two's Plymouth Argyle.