Surprisingly, the first opening fell for Panama as good work down the right found Anibal Godoy unmarked in the box, but he missed the chance to put them ahead with a horrid finish.
It was only a matter of time before England took control and, on eight minutes, John Stones snuck forward from a corner to head home unmarked.
A curling shot from Edgar Barcenas brought a few nervy looks for the English faithful as it narrowly evaded the goal of Jordan Pickford after 15 minutes.
The Three Lions were awarded a penalty when Jesse Lingard was brought down in the box, allowing Kane to step up and convert the penalty for his third goal of the tournament.
England found their third goal minutes later as a few passes played in Lingard, who curled home a superb strike from around 25 yards out.
It was 4-0 soon after as Stones capitalised on poor goalkeeping from Jamei Penedo to head home his second from a corner after Raheem Sterling's initial effort was blocked.
England grabbed their fifth through another penalty after Kane was man-handling inside the box. The captain stepped up once again and his sent his spot-kick into the same corner.
Kane became only the third English player to find a hat-trick at the World Cup, as he deflected home the sixth of the day following a shot by Ruben Loftus-Cheek.
Michael Murillo threatened for Panama's first ever goal at the World Cup, but Jordan Pickford - aided by his defence - rallied back to avert the danger.
Panama's wish was finally made true when substitute Felipe Baloy neatly tucked home a low delivery from the right after edging ahead of the last defender after 76 minutes for the nation's first ever finals goal.
The end result leaves the game as the highest scoring affair at the tournament in its two weeks so far, as Gareth Southgate’s men join Belgium in the second round.
England: Penedo, Murillo, Torres, Escobar, Davis, Gomez, Barcenas, Cooper, Godoy, Rodriguez, Perez.
Panama: Pickford, Trippier, Walker, Stones, Maguire, Young, Henderson, Loftus-Cheek, Lingard, Sterling, Kane.