England edge past Tunisia and Belgium stroll to victory
Kane came to England's rescue, while Belgium and Swedend also bagged World Cup wins.
Sweden got off to a winning start in Russia thanks to Andreas Granqvist's second-half penalty.
The Scandinavians enjoyed the better of proceedings in the first half in Nizhny Novgorod but struggled to beat South Korea's impressive goalkeeper Cho Hyun-woo.
Sweden continued to dominate after the break and finally edged in front when Granqvist converted from the spot following an extensive VAR review.
Manchester United forward Romelu Lukaku struck twice as Belgium defeated Panama 3-0.
The much-fancied Red Devils toiled during the first half as World Cup debutants Panama held firm at the back.
But Napoli attacker Dries Mertens scored a stunning volley after the break to open the deadlock, with Lukaku adding a second soon after when he headed in Kevin De Bruyne's tempting cross.
Lukaku put the result beyond doubt as the Central Americans tired late on when he latched on to a through ball before chipping coolly over the keeper.
Harry Kane scored twice as England edged past Tunisia in their tournament opener.
Gareth Southgate's men got off to a flying start when Spurs frontman Kane pounced on a rebound from a corner to tap home from close range.
But Tunisia drew level on 35 minutes when Ferjani Sassi dispatched a penalty after Kyle Walker caught Fakhreddine Ben Youssef with a stray arm in the box.
After the interval, England struggled to create clear-cut chances until the 90th minute when captain Kane again was quickest to react from a corner and headed high into the net.