Four Everton players were on international duty on Saturday, with Jordan Pickford and Lucas Digne figuring in satisfying away victories for their countries.
Andre Gomes remained on the bench as defending champions Portugal eased past Croatia 4-1 in their opening Nations League encounter in Porto.
Midfielder Gomes will hope to add to his 29-cap haul when Portugal visit Sweden on Tuesday.
Jonas Lossl was an unused substitute for Denmark in a 2-0 Nations League defeat by Belgium in Copenhagen.
Lyon defender Jason Denayer and Dries Mertens of Napoli were on target either side of half-time for the Belgians in a tight contest.
Everton goalkeeper Lossl, who understudies Kasper Schmeichel with his national team, will remain in Denmark for a home meeting with England on Tuesday.
Iceland 0-1 ENGLAND
Minutes played: 90
Pickford recorded his 11th shutout in 25 international appearances as England successfully navigated a hazardous Nations League opener in Iceland.
Gareth Southgate’s side were high on possession but short on creativity in Reykjavic in the Three Lions’ first fixture since November last year.
The severity of England’s task was exacerbated by the absence of a VAR, who would have ruled in the away team’s favour when Harry Kane’s early goal was errantly ruled out for offside.
England persevered, however – and overcame the dismissal of Kyle Walker for a second booking with 20 minutes remaining – to make their breakthrough in the first minute of time added on.
Defender Sverrir Ingason received his second yellow card for handling Raheem Sterling’s shot in the box.
And Manchester City forward Sterling beat goalkeeper Hannes Halldorsson with a penalty rolled down the middle.
Iceland had a glorious chance to instantly hit back when Joe Gomez was penalised for felling Holmbert Fridjonsson in the penalty area.
Where Sterling succeeded, though, former Aston Villa midfielder Birkir Bjarnason failed, blazing over from 12 yards.
England stay in Scandinavia to face Denmark in their second match in the competition on Tuesday.
Sweden 0-1 FRANCE
Minutes played: 90
Digne claimed the hotly-contested France left-back spot ahead of Bayern Munich’s Lucas Hernandez and helped Didier Deschamps’ world champions to an efficient single-goal Nations League win in Stockholm.
Kylian Mbappe provided the decisive strike, shooting home from six yards four minutes before half-time.
France withstood Sweden’s search for a second-half equaliser and could have extended their lead deep into stoppage time when Antoine Griezmann was off target with a penalty after Victor Lindelof fouled Manchester United colleague Anthony Martial in the area.
Digne, who earned his 31st senior cap against Sweden, returns to his homeland for a meeting with Croatia in Paris on Tuesday night.