England face Ghana in their second group game on 23 June at 21:00 BST.
Bayern Munich’s Kane gave England the lead with a retaken penalty early in the first half, before scoring a powerful header to restore his side’s lead three minutes before the break.
“I’m absolutely delighted that Kane equalled my record,” Lineker continued. “His all-round game is, for me, what separates him from all the others.”
Kane’s standout performance comes after Lionel Messi scored a hat-trick for Argentina against Algeria, Kylian Mbappe opened his account for France with two goals in the win over Senegal and Manchester City’s Erling Haaland also scored a brace in Norway’s victory against Iran.
Lineker’s co-host Alan Shearer, who scored 30 goals for England including two at the 1998 World Cup, said: “Harry Kane has seen Messi, Mbappe and Haaland all come on straight away and get the goals.
“It’s only a matter of time before he breaks your record.”
Manchester United defender Harry Maguire, who was left out of England boss Thomas Tuchel’s squad for this summer’s tournament, said Kane is not just the Three Lions’ best player, he’s “one of the best players in the world”.
He added: “You can’t speak highly enough of him. On the pitch, he’s unbelievable, but, off the pitch, he’s a massive leader.”
