In Sunday's 3-0 victory at Al Bayt Stadium, the Tottenham forward scored his team's second goal, setting up a meeting between France and Qatar in the quarterfinals of the tournament in 2022.
After winning the Golden Boot award in Russia four years ago, Kane's first World Cup goal this year brought his total to seven in 10 games.
The forward's 11 goals in major competitions are one higher than Lineker's total and include four goals for England during their run to the Euro 2020 final the previous year.
With 52 goals in 79 appearances, the 29-year-old is currently one goal away from tying Wayne Rooney (53) as England's all-time leading scorer.